KILLED proof of input_FHoq09Dlsx.trs # AProVE Commit ID: 5b976082cb74a395683ed8cc7acf94bd611ab29f fuhs 20230524 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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), 52 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), 5 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 27.2 s] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 38.6 s] (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), 563 ms] (38) CpxTypedWeightedCompleteTrs (39) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) InliningProof [UPPER BOUND(ID), 1143 ms] (42) CpxRNTS (43) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CpxRNTS (45) CompletionProof [UPPER BOUND(ID), 49 ms] (46) CpxTypedWeightedCompleteTrs (47) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (48) CpxRNTS (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 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), 8 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), 2 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 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) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms] (92) CdtProblem (93) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms] (98) CdtProblem (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6 ms] (112) CdtProblem (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 36 ms] (140) CdtProblem (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 35 ms] (148) CdtProblem (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 24 ms] (152) CdtProblem (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms] (156) CdtProblem (157) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 66 ms] (160) CdtProblem (161) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms] (164) CdtProblem (165) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 52 ms] (170) CdtProblem (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27 ms] (174) CdtProblem (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 33 ms] (178) CdtProblem (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (180) CdtProblem (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 81 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms] (184) CdtProblem (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms] (186) CdtProblem (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 2 ms] (188) CdtProblem (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 59 ms] (190) CdtProblem (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 11 ms] (192) CdtProblem (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 93 ms] (194) CdtProblem (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (196) CdtProblem (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (200) CdtProblem (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (202) CdtProblem (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms] (204) CdtProblem (205) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (206) CdtProblem (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 85 ms] (208) CdtProblem (209) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (210) CdtProblem (211) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 56 ms] (212) CdtProblem (213) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 6 ms] (214) CdtProblem (215) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (216) CdtProblem (217) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (218) CdtProblem (219) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 68 ms] (220) CdtProblem (221) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms] (222) CdtProblem (223) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms] (224) CdtProblem (225) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 9 ms] (226) CdtProblem (227) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 50 ms] (228) CdtProblem (229) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (230) CdtProblem (231) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (232) CdtProblem (233) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (234) CdtProblem (235) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 80 ms] (236) CdtProblem (237) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (238) CdtProblem (239) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (240) CpxWeightedTrs (241) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (242) CpxTypedWeightedTrs (243) CompletionProof [UPPER BOUND(ID), 1 ms] (244) CpxTypedWeightedCompleteTrs (245) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (246) CpxRNTS (247) CompletionProof [UPPER BOUND(ID), 6 ms] (248) CpxTypedWeightedCompleteTrs (249) NarrowingProof [BOTH BOUNDS(ID, ID), 68 ms] (250) CpxTypedWeightedCompleteTrs (251) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 33 ms] (252) CpxRNTS (253) InliningProof [UPPER BOUND(ID), 442 ms] (254) CpxRNTS (255) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (256) 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__U11(tt, L) -> a__U12(tt, L) a__U12(tt, L) -> s(a__length(mark(L))) a__U21(tt, IL, M, N) -> a__U22(tt, IL, M, N) a__U22(tt, IL, M, N) -> a__U23(tt, IL, M, N) a__U23(tt, IL, M, N) -> cons(mark(N), take(M, IL)) a__length(nil) -> 0 a__length(cons(N, L)) -> a__U11(tt, L) a__take(0, IL) -> nil a__take(s(M), cons(N, IL)) -> a__U21(tt, IL, M, N) mark(zeros) -> a__zeros mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X1, X2)) -> a__U12(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) 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(s(X)) -> s(mark(X)) mark(nil) -> nil a__zeros -> zeros a__U11(X1, X2) -> U11(X1, X2) a__U12(X1, X2) -> U12(X1, X2) a__length(X) -> length(X) a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) 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__U11(tt, L) -> a__U12(tt, L) a__U12(tt, L) -> s(a__length(mark(L))) a__U21(tt, IL, M, N) -> a__U22(tt, IL, M, N) a__U22(tt, IL, M, N) -> a__U23(tt, IL, M, N) a__U23(tt, IL, M, N) -> cons(mark(N), take(M, IL)) a__length(nil) -> 0' a__length(cons(N, L)) -> a__U11(tt, L) a__take(0', IL) -> nil a__take(s(M), cons(N, IL)) -> a__U21(tt, IL, M, N) mark(zeros) -> a__zeros mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X1, X2)) -> a__U12(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) 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(s(X)) -> s(mark(X)) mark(nil) -> nil a__zeros -> zeros a__U11(X1, X2) -> U11(X1, X2) a__U12(X1, X2) -> U12(X1, X2) a__length(X) -> length(X) a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) 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__U11(tt, L) -> a__U12(tt, L) a__U12(tt, L) -> s(a__length(mark(L))) a__U21(tt, IL, M, N) -> a__U22(tt, IL, M, N) a__U22(tt, IL, M, N) -> a__U23(tt, IL, M, N) a__U23(tt, IL, M, N) -> cons(mark(N), take(M, IL)) a__length(nil) -> 0 a__length(cons(N, L)) -> a__U11(tt, L) a__take(0, IL) -> nil a__take(s(M), cons(N, IL)) -> a__U21(tt, IL, M, N) mark(zeros) -> a__zeros mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X1, X2)) -> a__U12(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) 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(s(X)) -> s(mark(X)) mark(nil) -> nil a__zeros -> zeros a__U11(X1, X2) -> U11(X1, X2) a__U12(X1, X2) -> U12(X1, X2) a__length(X) -> length(X) a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) 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__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U11(z0, z1) -> c3 A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U12(z0, z1) -> c5 A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U21(z0, z1, z2, z3) -> c7 A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U22(z0, z1, z2, z3) -> c9 A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__U23(z0, z1, z2, z3) -> c11 A__LENGTH(nil) -> c12 A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__LENGTH(z0) -> c14 A__TAKE(0, z0) -> c15 A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) A__TAKE(z0, z1) -> c17 MARK(zeros) -> c18(A__ZEROS) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(0) -> c28 MARK(tt) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 S tuples: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U11(z0, z1) -> c3 A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U12(z0, z1) -> c5 A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U21(z0, z1, z2, z3) -> c7 A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U22(z0, z1, z2, z3) -> c9 A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__U23(z0, z1, z2, z3) -> c11 A__LENGTH(nil) -> c12 A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__LENGTH(z0) -> c14 A__TAKE(0, z0) -> c15 A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) A__TAKE(z0, z1) -> c17 MARK(zeros) -> c18(A__ZEROS) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(0) -> c28 MARK(tt) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__ZEROS, A__U11_2, A__U12_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1 Compound Symbols: c, c1, c2_1, c3, c4_2, c5, c6_1, c7, c8_1, c9, c10_1, c11, c12, c13_1, c14, c15, c16_1, c17, c18_1, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c28, c29, c30_1, c31 ---------------------------------------- (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__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U11(z0, z1) -> c3 A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U12(z0, z1) -> c5 A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U21(z0, z1, z2, z3) -> c7 A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U22(z0, z1, z2, z3) -> c9 A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__U23(z0, z1, z2, z3) -> c11 A__LENGTH(nil) -> c12 A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__LENGTH(z0) -> c14 A__TAKE(0, z0) -> c15 A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) A__TAKE(z0, z1) -> c17 MARK(zeros) -> c18(A__ZEROS) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(0) -> c28 MARK(tt) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 The (relative) TRS S consists of the following rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil 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__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U11(z0, z1) -> c3 A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U12(z0, z1) -> c5 A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U21(z0, z1, z2, z3) -> c7 A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U22(z0, z1, z2, z3) -> c9 A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__U23(z0, z1, z2, z3) -> c11 A__LENGTH(nil) -> c12 A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__LENGTH(z0) -> c14 A__TAKE(0', z0) -> c15 A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) A__TAKE(z0, z1) -> c17 MARK(zeros) -> c18(A__ZEROS) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(0') -> c28 MARK(tt) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 The (relative) TRS S consists of the following rules: a__zeros -> cons(0', zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0' a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Rewrite Strategy: INNERMOST ---------------------------------------- (11) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (12) Obligation: Innermost TRS: Rules: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U11(z0, z1) -> c3 A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U12(z0, z1) -> c5 A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U21(z0, z1, z2, z3) -> c7 A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U22(z0, z1, z2, z3) -> c9 A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__U23(z0, z1, z2, z3) -> c11 A__LENGTH(nil) -> c12 A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__LENGTH(z0) -> c14 A__TAKE(0', z0) -> c15 A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) A__TAKE(z0, z1) -> c17 MARK(zeros) -> c18(A__ZEROS) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(0') -> c28 MARK(tt) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 a__zeros -> cons(0', zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0' a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Types: A__ZEROS :: c:c1 c :: c:c1 c1 :: c:c1 A__U11 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c2:c3 tt :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c2 :: c4:c5 -> c2:c3 A__U12 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c4:c5 c3 :: c2:c3 c4 :: c12:c13:c14 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c4:c5 A__LENGTH :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c12:c13:c14 mark :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take MARK :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c5 :: c4:c5 A__U21 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c6:c7 c6 :: c8:c9 -> c6:c7 A__U22 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c8:c9 c7 :: c6:c7 c8 :: c10:c11 -> c8:c9 A__U23 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c10:c11 c9 :: c8:c9 c10 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c10:c11 c11 :: c10:c11 nil :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c12 :: c12:c13:c14 cons :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c13 :: c2:c3 -> c12:c13:c14 c14 :: c12:c13:c14 A__TAKE :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c15:c16:c17 0' :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c15 :: c15:c16:c17 s :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c16 :: c6:c7 -> c15:c16:c17 c17 :: c15:c16:c17 zeros :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c18 :: c:c1 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U11 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c19 :: c2:c3 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U12 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c20 :: c4:c5 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 length :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c21 :: c12:c13:c14 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U21 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c22 :: c6:c7 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U22 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c23 :: c8:c9 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U23 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c24 :: c10:c11 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 take :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c25 :: c15:c16:c17 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c26 :: c15:c16:c17 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c27 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c28 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c29 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c30 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c31 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 a__zeros :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U11 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U12 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__length :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U21 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U22 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U23 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__take :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take hole_c:c11_32 :: c:c1 hole_c2:c32_32 :: c2:c3 hole_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take3_32 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take hole_c4:c54_32 :: c4:c5 hole_c12:c13:c145_32 :: c12:c13:c14 hole_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c316_32 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 hole_c6:c77_32 :: c6:c7 hole_c8:c98_32 :: c8:c9 hole_c10:c119_32 :: c10:c11 hole_c15:c16:c1710_32 :: c15:c16:c17 gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32 :: Nat -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take gen_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3112_32 :: Nat -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 ---------------------------------------- (13) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: A__U11, A__U12, A__LENGTH, mark, MARK, A__U21, A__U22, A__U23, a__U11, a__U12, a__length, a__U21, a__U22, a__U23 They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__LENGTH A__U11 = MARK A__U11 = A__U21 A__U11 = A__U22 A__U11 = A__U23 A__U12 = A__LENGTH mark < A__U12 A__U12 = MARK A__U12 = A__U21 A__U12 = A__U22 A__U12 = A__U23 A__LENGTH = MARK A__LENGTH = A__U21 A__LENGTH = A__U22 A__LENGTH = A__U23 mark < MARK mark = a__U11 mark = a__U12 mark = a__length mark = a__U21 mark = a__U22 mark = a__U23 MARK = A__U21 MARK = A__U22 MARK = A__U23 A__U21 = A__U22 A__U21 = A__U23 A__U22 = A__U23 a__U11 = a__U12 a__U11 = a__length a__U11 = a__U21 a__U11 = a__U22 a__U11 = a__U23 a__U12 = a__length a__U12 = a__U21 a__U12 = a__U22 a__U12 = a__U23 a__length = a__U21 a__length = a__U22 a__length = a__U23 a__U21 = a__U22 a__U21 = a__U23 a__U22 = a__U23 ---------------------------------------- (14) Obligation: Innermost TRS: Rules: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U11(z0, z1) -> c3 A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U12(z0, z1) -> c5 A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U21(z0, z1, z2, z3) -> c7 A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U22(z0, z1, z2, z3) -> c9 A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__U23(z0, z1, z2, z3) -> c11 A__LENGTH(nil) -> c12 A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__LENGTH(z0) -> c14 A__TAKE(0', z0) -> c15 A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) A__TAKE(z0, z1) -> c17 MARK(zeros) -> c18(A__ZEROS) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(0') -> c28 MARK(tt) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 a__zeros -> cons(0', zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0' a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Types: A__ZEROS :: c:c1 c :: c:c1 c1 :: c:c1 A__U11 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c2:c3 tt :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c2 :: c4:c5 -> c2:c3 A__U12 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c4:c5 c3 :: c2:c3 c4 :: c12:c13:c14 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c4:c5 A__LENGTH :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c12:c13:c14 mark :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take MARK :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c5 :: c4:c5 A__U21 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c6:c7 c6 :: c8:c9 -> c6:c7 A__U22 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c8:c9 c7 :: c6:c7 c8 :: c10:c11 -> c8:c9 A__U23 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c10:c11 c9 :: c8:c9 c10 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c10:c11 c11 :: c10:c11 nil :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c12 :: c12:c13:c14 cons :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c13 :: c2:c3 -> c12:c13:c14 c14 :: c12:c13:c14 A__TAKE :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c15:c16:c17 0' :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c15 :: c15:c16:c17 s :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c16 :: c6:c7 -> c15:c16:c17 c17 :: c15:c16:c17 zeros :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c18 :: c:c1 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U11 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c19 :: c2:c3 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U12 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c20 :: c4:c5 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 length :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c21 :: c12:c13:c14 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U21 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c22 :: c6:c7 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U22 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c23 :: c8:c9 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U23 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c24 :: c10:c11 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 take :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c25 :: c15:c16:c17 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c26 :: c15:c16:c17 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c27 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c28 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c29 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c30 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c31 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 a__zeros :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U11 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U12 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__length :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U21 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U22 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U23 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__take :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take hole_c:c11_32 :: c:c1 hole_c2:c32_32 :: c2:c3 hole_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take3_32 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take hole_c4:c54_32 :: c4:c5 hole_c12:c13:c145_32 :: c12:c13:c14 hole_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c316_32 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 hole_c6:c77_32 :: c6:c7 hole_c8:c98_32 :: c8:c9 hole_c10:c119_32 :: c10:c11 hole_c15:c16:c1710_32 :: c15:c16:c17 gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32 :: Nat -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take gen_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3112_32 :: Nat -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 Generator Equations: gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(0) <=> tt gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(+(x, 1)) <=> cons(gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(x), tt) gen_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3112_32(0) <=> c18(c) gen_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3112_32(+(x, 1)) <=> c19(c2(c4(c12, c18(c))), gen_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3112_32(x)) The following defined symbols remain to be analysed: a__U11, A__U11, A__U12, A__LENGTH, mark, MARK, A__U21, A__U22, A__U23, a__U12, a__length, a__U21, a__U22, a__U23 They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__LENGTH A__U11 = MARK A__U11 = A__U21 A__U11 = A__U22 A__U11 = A__U23 A__U12 = A__LENGTH mark < A__U12 A__U12 = MARK A__U12 = A__U21 A__U12 = A__U22 A__U12 = A__U23 A__LENGTH = MARK A__LENGTH = A__U21 A__LENGTH = A__U22 A__LENGTH = A__U23 mark < MARK mark = a__U11 mark = a__U12 mark = a__length mark = a__U21 mark = a__U22 mark = a__U23 MARK = A__U21 MARK = A__U22 MARK = A__U23 A__U21 = A__U22 A__U21 = A__U23 A__U22 = A__U23 a__U11 = a__U12 a__U11 = a__length a__U11 = a__U21 a__U11 = a__U22 a__U11 = a__U23 a__U12 = a__length a__U12 = a__U21 a__U12 = a__U22 a__U12 = a__U23 a__length = a__U21 a__length = a__U22 a__length = a__U23 a__U21 = a__U22 a__U21 = a__U23 a__U22 = a__U23 ---------------------------------------- (15) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(n2246130_32)) -> gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(n2246130_32), rt in Omega(0) Induction Base: mark(gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(0)) ->_R^Omega(0) tt Induction Step: mark(gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(+(n2246130_32, 1))) ->_R^Omega(0) cons(mark(gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(n2246130_32)), tt) ->_IH cons(gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(c2246131_32), tt) 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__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U11(z0, z1) -> c3 A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U12(z0, z1) -> c5 A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U21(z0, z1, z2, z3) -> c7 A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U22(z0, z1, z2, z3) -> c9 A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__U23(z0, z1, z2, z3) -> c11 A__LENGTH(nil) -> c12 A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__LENGTH(z0) -> c14 A__TAKE(0', z0) -> c15 A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) A__TAKE(z0, z1) -> c17 MARK(zeros) -> c18(A__ZEROS) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(0') -> c28 MARK(tt) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 a__zeros -> cons(0', zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0' a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Types: A__ZEROS :: c:c1 c :: c:c1 c1 :: c:c1 A__U11 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c2:c3 tt :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c2 :: c4:c5 -> c2:c3 A__U12 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c4:c5 c3 :: c2:c3 c4 :: c12:c13:c14 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c4:c5 A__LENGTH :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c12:c13:c14 mark :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take MARK :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c5 :: c4:c5 A__U21 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c6:c7 c6 :: c8:c9 -> c6:c7 A__U22 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c8:c9 c7 :: c6:c7 c8 :: c10:c11 -> c8:c9 A__U23 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c10:c11 c9 :: c8:c9 c10 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c10:c11 c11 :: c10:c11 nil :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c12 :: c12:c13:c14 cons :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c13 :: c2:c3 -> c12:c13:c14 c14 :: c12:c13:c14 A__TAKE :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c15:c16:c17 0' :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c15 :: c15:c16:c17 s :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c16 :: c6:c7 -> c15:c16:c17 c17 :: c15:c16:c17 zeros :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c18 :: c:c1 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U11 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c19 :: c2:c3 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U12 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c20 :: c4:c5 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 length :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c21 :: c12:c13:c14 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U21 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c22 :: c6:c7 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U22 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c23 :: c8:c9 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U23 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c24 :: c10:c11 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 take :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c25 :: c15:c16:c17 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c26 :: c15:c16:c17 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c27 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c28 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c29 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c30 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c31 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 a__zeros :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U11 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U12 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__length :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U21 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U22 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U23 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__take :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take hole_c:c11_32 :: c:c1 hole_c2:c32_32 :: c2:c3 hole_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take3_32 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take hole_c4:c54_32 :: c4:c5 hole_c12:c13:c145_32 :: c12:c13:c14 hole_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c316_32 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 hole_c6:c77_32 :: c6:c7 hole_c8:c98_32 :: c8:c9 hole_c10:c119_32 :: c10:c11 hole_c15:c16:c1710_32 :: c15:c16:c17 gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32 :: Nat -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take gen_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3112_32 :: Nat -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 Lemmas: mark(gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(n2246130_32)) -> gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(n2246130_32), rt in Omega(0) Generator Equations: gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(0) <=> tt gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(+(x, 1)) <=> cons(gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(x), tt) gen_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3112_32(0) <=> c18(c) gen_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3112_32(+(x, 1)) <=> c19(c2(c4(c12, c18(c))), gen_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3112_32(x)) The following defined symbols remain to be analysed: a__U21, A__U11, A__U12, A__LENGTH, MARK, A__U21, A__U22, A__U23, a__U11, a__U12, a__length, a__U22, a__U23 They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__LENGTH A__U11 = MARK A__U11 = A__U21 A__U11 = A__U22 A__U11 = A__U23 A__U12 = A__LENGTH mark < A__U12 A__U12 = MARK A__U12 = A__U21 A__U12 = A__U22 A__U12 = A__U23 A__LENGTH = MARK A__LENGTH = A__U21 A__LENGTH = A__U22 A__LENGTH = A__U23 mark < MARK mark = a__U11 mark = a__U12 mark = a__length mark = a__U21 mark = a__U22 mark = a__U23 MARK = A__U21 MARK = A__U22 MARK = A__U23 A__U21 = A__U22 A__U21 = A__U23 A__U22 = A__U23 a__U11 = a__U12 a__U11 = a__length a__U11 = a__U21 a__U11 = a__U22 a__U11 = a__U23 a__U12 = a__length a__U12 = a__U21 a__U12 = a__U22 a__U12 = a__U23 a__length = a__U21 a__length = a__U22 a__length = a__U23 a__U21 = a__U22 a__U21 = a__U23 a__U22 = a__U23 ---------------------------------------- (17) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: MARK(gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(+(1, n4472469_32))) -> *13_32, rt in Omega(n4472469_32) Induction Base: MARK(gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(+(1, 0))) Induction Step: MARK(gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(+(1, +(n4472469_32, 1)))) ->_R^Omega(1) c27(MARK(gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(+(1, n4472469_32)))) ->_IH c27(*13_32) 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__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U11(z0, z1) -> c3 A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U12(z0, z1) -> c5 A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U21(z0, z1, z2, z3) -> c7 A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U22(z0, z1, z2, z3) -> c9 A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__U23(z0, z1, z2, z3) -> c11 A__LENGTH(nil) -> c12 A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__LENGTH(z0) -> c14 A__TAKE(0', z0) -> c15 A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) A__TAKE(z0, z1) -> c17 MARK(zeros) -> c18(A__ZEROS) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(0') -> c28 MARK(tt) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 a__zeros -> cons(0', zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0' a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Types: A__ZEROS :: c:c1 c :: c:c1 c1 :: c:c1 A__U11 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c2:c3 tt :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c2 :: c4:c5 -> c2:c3 A__U12 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c4:c5 c3 :: c2:c3 c4 :: c12:c13:c14 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c4:c5 A__LENGTH :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c12:c13:c14 mark :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take MARK :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c5 :: c4:c5 A__U21 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c6:c7 c6 :: c8:c9 -> c6:c7 A__U22 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c8:c9 c7 :: c6:c7 c8 :: c10:c11 -> c8:c9 A__U23 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c10:c11 c9 :: c8:c9 c10 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c10:c11 c11 :: c10:c11 nil :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c12 :: c12:c13:c14 cons :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c13 :: c2:c3 -> c12:c13:c14 c14 :: c12:c13:c14 A__TAKE :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c15:c16:c17 0' :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c15 :: c15:c16:c17 s :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c16 :: c6:c7 -> c15:c16:c17 c17 :: c15:c16:c17 zeros :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c18 :: c:c1 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U11 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c19 :: c2:c3 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U12 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c20 :: c4:c5 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 length :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c21 :: c12:c13:c14 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U21 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c22 :: c6:c7 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U22 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c23 :: c8:c9 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U23 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c24 :: c10:c11 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 take :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c25 :: c15:c16:c17 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c26 :: c15:c16:c17 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c27 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c28 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c29 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c30 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c31 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 a__zeros :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U11 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U12 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__length :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U21 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U22 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U23 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__take :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take hole_c:c11_32 :: c:c1 hole_c2:c32_32 :: c2:c3 hole_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take3_32 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take hole_c4:c54_32 :: c4:c5 hole_c12:c13:c145_32 :: c12:c13:c14 hole_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c316_32 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 hole_c6:c77_32 :: c6:c7 hole_c8:c98_32 :: c8:c9 hole_c10:c119_32 :: c10:c11 hole_c15:c16:c1710_32 :: c15:c16:c17 gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32 :: Nat -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take gen_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3112_32 :: Nat -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 Lemmas: mark(gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(n2246130_32)) -> gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(n2246130_32), rt in Omega(0) Generator Equations: gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(0) <=> tt gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(+(x, 1)) <=> cons(gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(x), tt) gen_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3112_32(0) <=> c18(c) gen_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3112_32(+(x, 1)) <=> c19(c2(c4(c12, c18(c))), gen_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3112_32(x)) The following defined symbols remain to be analysed: MARK, A__U21, A__U22, A__U23 They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__LENGTH A__U11 = MARK A__U11 = A__U21 A__U11 = A__U22 A__U11 = A__U23 A__U12 = A__LENGTH A__U12 = MARK A__U12 = A__U21 A__U12 = A__U22 A__U12 = A__U23 A__LENGTH = MARK A__LENGTH = A__U21 A__LENGTH = A__U22 A__LENGTH = A__U23 MARK = A__U21 MARK = A__U22 MARK = A__U23 A__U21 = A__U22 A__U21 = A__U23 A__U22 = A__U23 ---------------------------------------- (20) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (21) BOUNDS(n^1, INF) ---------------------------------------- (22) Obligation: Innermost TRS: Rules: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U11(z0, z1) -> c3 A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U12(z0, z1) -> c5 A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U21(z0, z1, z2, z3) -> c7 A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U22(z0, z1, z2, z3) -> c9 A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__U23(z0, z1, z2, z3) -> c11 A__LENGTH(nil) -> c12 A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__LENGTH(z0) -> c14 A__TAKE(0', z0) -> c15 A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) A__TAKE(z0, z1) -> c17 MARK(zeros) -> c18(A__ZEROS) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(0') -> c28 MARK(tt) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 a__zeros -> cons(0', zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0' a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Types: A__ZEROS :: c:c1 c :: c:c1 c1 :: c:c1 A__U11 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c2:c3 tt :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c2 :: c4:c5 -> c2:c3 A__U12 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c4:c5 c3 :: c2:c3 c4 :: c12:c13:c14 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c4:c5 A__LENGTH :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c12:c13:c14 mark :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take MARK :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c5 :: c4:c5 A__U21 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c6:c7 c6 :: c8:c9 -> c6:c7 A__U22 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c8:c9 c7 :: c6:c7 c8 :: c10:c11 -> c8:c9 A__U23 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c10:c11 c9 :: c8:c9 c10 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c10:c11 c11 :: c10:c11 nil :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c12 :: c12:c13:c14 cons :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c13 :: c2:c3 -> c12:c13:c14 c14 :: c12:c13:c14 A__TAKE :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> c15:c16:c17 0' :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c15 :: c15:c16:c17 s :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c16 :: c6:c7 -> c15:c16:c17 c17 :: c15:c16:c17 zeros :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c18 :: c:c1 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U11 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c19 :: c2:c3 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U12 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c20 :: c4:c5 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 length :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c21 :: c12:c13:c14 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U21 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c22 :: c6:c7 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U22 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c23 :: c8:c9 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 U23 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c24 :: c10:c11 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 take :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take c25 :: c15:c16:c17 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c26 :: c15:c16:c17 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c27 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c28 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c29 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c30 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 c31 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 a__zeros :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U11 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U12 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__length :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U21 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U22 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__U23 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take a__take :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take hole_c:c11_32 :: c:c1 hole_c2:c32_32 :: c2:c3 hole_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take3_32 :: tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take hole_c4:c54_32 :: c4:c5 hole_c12:c13:c145_32 :: c12:c13:c14 hole_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c316_32 :: c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 hole_c6:c77_32 :: c6:c7 hole_c8:c98_32 :: c8:c9 hole_c10:c119_32 :: c10:c11 hole_c15:c16:c1710_32 :: c15:c16:c17 gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32 :: Nat -> tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take gen_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3112_32 :: Nat -> c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 Lemmas: mark(gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(n2246130_32)) -> gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(n2246130_32), rt in Omega(0) MARK(gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(+(1, n4472469_32))) -> *13_32, rt in Omega(n4472469_32) Generator Equations: gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(0) <=> tt gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(+(x, 1)) <=> cons(gen_tt:nil:cons:0':s:zeros:U11:U12:length:U21:U22:U23:take11_32(x), tt) gen_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3112_32(0) <=> c18(c) gen_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3112_32(+(x, 1)) <=> c19(c2(c4(c12, c18(c))), gen_c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3112_32(x)) The following defined symbols remain to be analysed: A__U21, A__U11, A__U12, A__LENGTH, A__U22, A__U23 They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__LENGTH A__U11 = MARK A__U11 = A__U21 A__U11 = A__U22 A__U11 = A__U23 A__U12 = A__LENGTH A__U12 = MARK A__U12 = A__U21 A__U12 = A__U22 A__U12 = A__U23 A__LENGTH = MARK A__LENGTH = A__U21 A__LENGTH = A__U22 A__LENGTH = A__U23 MARK = A__U21 MARK = A__U22 MARK = A__U23 A__U21 = A__U22 A__U21 = A__U23 A__U22 = A__U23 ---------------------------------------- (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__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U11(z0, z1) -> c3 A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U12(z0, z1) -> c5 A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U21(z0, z1, z2, z3) -> c7 A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U22(z0, z1, z2, z3) -> c9 A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__U23(z0, z1, z2, z3) -> c11 A__LENGTH(nil) -> c12 A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__LENGTH(z0) -> c14 A__TAKE(0, z0) -> c15 A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) A__TAKE(z0, z1) -> c17 MARK(zeros) -> c18(A__ZEROS) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(0) -> c28 MARK(tt) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 S tuples: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U11(z0, z1) -> c3 A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U12(z0, z1) -> c5 A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U21(z0, z1, z2, z3) -> c7 A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U22(z0, z1, z2, z3) -> c9 A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__U23(z0, z1, z2, z3) -> c11 A__LENGTH(nil) -> c12 A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__LENGTH(z0) -> c14 A__TAKE(0, z0) -> c15 A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) A__TAKE(z0, z1) -> c17 MARK(zeros) -> c18(A__ZEROS) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(0) -> c28 MARK(tt) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__ZEROS, A__U11_2, A__U12_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1 Compound Symbols: c, c1, c2_1, c3, c4_2, c5, c6_1, c7, c8_1, c9, c10_1, c11, c12, c13_1, c14, c15, c16_1, c17, c18_1, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c28, c29, c30_1, c31 ---------------------------------------- (25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 15 trailing nodes: MARK(nil) -> c31 A__U22(z0, z1, z2, z3) -> c9 A__U21(z0, z1, z2, z3) -> c7 A__TAKE(0, z0) -> c15 A__U23(z0, z1, z2, z3) -> c11 A__LENGTH(z0) -> c14 A__ZEROS -> c A__ZEROS -> c1 MARK(0) -> c28 A__LENGTH(nil) -> c12 A__U11(z0, z1) -> c3 MARK(zeros) -> c18(A__ZEROS) MARK(tt) -> c29 A__TAKE(z0, z1) -> c17 A__U12(z0, z1) -> c5 ---------------------------------------- (26) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U12_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1 Compound Symbols: c2_1, c4_2, c6_1, c8_1, c10_1, c13_1, c16_1, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_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__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) The (relative) TRS S consists of the following rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil 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__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil 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__U11(tt, z0) -> c2(A__U12(tt, z0)) [1] A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) [1] A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) [1] A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) [1] A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) [1] A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) [1] MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) [1] MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) [1] MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c27(MARK(z0)) [1] MARK(s(z0)) -> c30(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__U11(tt, z0) -> a__U12(tt, z0) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U12(tt, z0) -> s(a__length(mark(z0))) [0] a__U12(z0, z1) -> U12(z0, z1) [0] a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) [0] a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) [0] a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) [0] a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) [0] a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) [0] a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) [0] a__length(nil) -> 0 [0] a__length(cons(z0, z1)) -> a__U11(tt, z1) [0] a__length(z0) -> length(z0) [0] a__take(0, z0) -> nil [0] a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) [0] a__take(z0, z1) -> take(z0, z1) [0] mark(zeros) -> a__zeros [0] mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0] mark(U12(z0, z1)) -> a__U12(mark(z0), z1) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) [0] mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) [0] mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) [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(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [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__U11(tt, z0) -> c2(A__U12(tt, z0)) [1] A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) [1] A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) [1] A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) [1] A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) [1] A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) [1] MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) [1] MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) [1] MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c27(MARK(z0)) [1] MARK(s(z0)) -> c30(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__U11(tt, z0) -> a__U12(tt, z0) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U12(tt, z0) -> s(a__length(mark(z0))) [0] a__U12(z0, z1) -> U12(z0, z1) [0] a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) [0] a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) [0] a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) [0] a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) [0] a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) [0] a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) [0] a__length(nil) -> 0 [0] a__length(cons(z0, z1)) -> a__U11(tt, z1) [0] a__length(z0) -> length(z0) [0] a__take(0, z0) -> nil [0] a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) [0] a__take(z0, z1) -> take(z0, z1) [0] mark(zeros) -> a__zeros [0] mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0] mark(U12(z0, z1)) -> a__U12(mark(z0), z1) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) [0] mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) [0] mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) [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(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] The TRS has the following type information: A__U11 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> c2 tt :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil c2 :: c4 -> c2 A__U12 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> c4 c4 :: c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c4 A__LENGTH :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> c13 mark :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil MARK :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 A__U21 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> c6 c6 :: c8 -> c6 A__U22 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> c8 c8 :: c10 -> c8 A__U23 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> c10 c10 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c10 cons :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil c13 :: c2 -> c13 A__TAKE :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> c16 s :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil c16 :: c6 -> c16 U11 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil c19 :: c2 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 U12 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil c20 :: c4 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 length :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil c21 :: c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 U21 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil c22 :: c6 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 U22 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil c23 :: c8 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 U23 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil c24 :: c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 take :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil c25 :: c16 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 c26 :: c16 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 c27 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 c30 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 a__zeros :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil 0 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil zeros :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil a__U11 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil a__U12 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil a__length :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil a__U21 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil a__U22 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil a__U23 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil nil :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil a__take :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil -> tt:cons:s:U11:U12:length:U21:U22:U23: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__U11_2 A__U12_2 A__U21_4 A__U22_4 A__U23_4 A__LENGTH_1 A__TAKE_2 MARK_1 (c) The following functions are completely defined: a__zeros a__U11_2 a__U12_2 a__U21_4 a__U22_4 a__U23_4 a__length_1 a__take_2 mark_1 Due to the following rules being added: a__zeros -> null_a__zeros [0] a__U11(v0, v1) -> null_a__U11 [0] a__U12(v0, v1) -> null_a__U12 [0] a__U21(v0, v1, v2, v3) -> null_a__U21 [0] a__U22(v0, v1, v2, v3) -> null_a__U22 [0] a__U23(v0, v1, v2, v3) -> null_a__U23 [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__U11, null_a__U12, null_a__U21, null_a__U22, null_a__U23, null_a__length, null_a__take, null_mark, const, const1, const2, const3, const4, const5, const6, const7 ---------------------------------------- (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__U11(tt, z0) -> c2(A__U12(tt, z0)) [1] A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) [1] A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) [1] A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) [1] A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) [1] A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) [1] MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) [1] MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) [1] MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c27(MARK(z0)) [1] MARK(s(z0)) -> c30(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__U11(tt, z0) -> a__U12(tt, z0) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U12(tt, z0) -> s(a__length(mark(z0))) [0] a__U12(z0, z1) -> U12(z0, z1) [0] a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) [0] a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) [0] a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) [0] a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) [0] a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) [0] a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) [0] a__length(nil) -> 0 [0] a__length(cons(z0, z1)) -> a__U11(tt, z1) [0] a__length(z0) -> length(z0) [0] a__take(0, z0) -> nil [0] a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) [0] a__take(z0, z1) -> take(z0, z1) [0] mark(zeros) -> a__zeros [0] mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0] mark(U12(z0, z1)) -> a__U12(mark(z0), z1) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) [0] mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) [0] mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) [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(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] a__zeros -> null_a__zeros [0] a__U11(v0, v1) -> null_a__U11 [0] a__U12(v0, v1) -> null_a__U12 [0] a__U21(v0, v1, v2, v3) -> null_a__U21 [0] a__U22(v0, v1, v2, v3) -> null_a__U22 [0] a__U23(v0, v1, v2, v3) -> null_a__U23 [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__U11 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c2 tt :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c2 :: c4 -> c2 A__U12 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c4 c4 :: c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c4 A__LENGTH :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c13 mark :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark MARK :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 A__U21 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c6 c6 :: c8 -> c6 A__U22 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c8 c8 :: c10 -> c8 A__U23 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c10 c10 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c10 cons :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c13 :: c2 -> c13 A__TAKE :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c16 s :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c16 :: c6 -> c16 U11 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c19 :: c2 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 U12 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c20 :: c4 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 length :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c21 :: c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 U21 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c22 :: c6 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 U22 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c23 :: c8 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 U23 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c24 :: c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 take :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c25 :: c16 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 c26 :: c16 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 c27 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 c30 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 a__zeros :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark 0 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark zeros :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__U11 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__U12 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__length :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__U21 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__U22 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__U23 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark nil :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__take :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__zeros :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__U11 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__U12 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__U21 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__U22 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__U23 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__length :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__take :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_mark :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark const :: c2 const1 :: c4 const2 :: c13 const3 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 const4 :: c6 const5 :: c8 const6 :: c10 const7 :: c16 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__U11(tt, z0) -> c2(A__U12(tt, z0)) [1] A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros), MARK(zeros)) [1] A__U12(tt, U11(z0', z1')) -> c4(A__LENGTH(a__U11(mark(z0'), z1')), MARK(U11(z0', z1'))) [1] A__U12(tt, U12(z0'', z1'')) -> c4(A__LENGTH(a__U12(mark(z0''), z1'')), MARK(U12(z0'', z1''))) [1] A__U12(tt, length(z01)) -> c4(A__LENGTH(a__length(mark(z01))), MARK(length(z01))) [1] A__U12(tt, U21(z02, z11, z2', z3')) -> c4(A__LENGTH(a__U21(mark(z02), z11, z2', z3')), MARK(U21(z02, z11, z2', z3'))) [1] A__U12(tt, U22(z03, z12, z2'', z3'')) -> c4(A__LENGTH(a__U22(mark(z03), z12, z2'', z3'')), MARK(U22(z03, z12, z2'', z3''))) [1] A__U12(tt, U23(z04, z13, z21, z31)) -> c4(A__LENGTH(a__U23(mark(z04), z13, z21, z31)), MARK(U23(z04, z13, z21, z31))) [1] A__U12(tt, take(z05, z14)) -> c4(A__LENGTH(a__take(mark(z05), mark(z14))), MARK(take(z05, z14))) [1] A__U12(tt, cons(z06, z15)) -> c4(A__LENGTH(cons(mark(z06), z15)), MARK(cons(z06, z15))) [1] A__U12(tt, 0) -> c4(A__LENGTH(0), MARK(0)) [1] A__U12(tt, tt) -> c4(A__LENGTH(tt), MARK(tt)) [1] A__U12(tt, s(z07)) -> c4(A__LENGTH(s(mark(z07))), MARK(s(z07))) [1] A__U12(tt, nil) -> c4(A__LENGTH(nil), MARK(nil)) [1] A__U12(tt, z0) -> c4(A__LENGTH(null_mark), MARK(z0)) [1] A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) [1] A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) [1] A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) [1] A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) [1] MARK(U11(zeros, z1)) -> c19(A__U11(a__zeros, z1), MARK(zeros)) [1] MARK(U11(U11(z08, z16), z1)) -> c19(A__U11(a__U11(mark(z08), z16), z1), MARK(U11(z08, z16))) [1] MARK(U11(U12(z09, z17), z1)) -> c19(A__U11(a__U12(mark(z09), z17), z1), MARK(U12(z09, z17))) [1] MARK(U11(length(z010), z1)) -> c19(A__U11(a__length(mark(z010)), z1), MARK(length(z010))) [1] MARK(U11(U21(z011, z18, z22, z32), z1)) -> c19(A__U11(a__U21(mark(z011), z18, z22, z32), z1), MARK(U21(z011, z18, z22, z32))) [1] MARK(U11(U22(z012, z19, z23, z33), z1)) -> c19(A__U11(a__U22(mark(z012), z19, z23, z33), z1), MARK(U22(z012, z19, z23, z33))) [1] MARK(U11(U23(z013, z110, z24, z34), z1)) -> c19(A__U11(a__U23(mark(z013), z110, z24, z34), z1), MARK(U23(z013, z110, z24, z34))) [1] MARK(U11(take(z014, z111), z1)) -> c19(A__U11(a__take(mark(z014), mark(z111)), z1), MARK(take(z014, z111))) [1] MARK(U11(cons(z015, z112), z1)) -> c19(A__U11(cons(mark(z015), z112), z1), MARK(cons(z015, z112))) [1] MARK(U11(0, z1)) -> c19(A__U11(0, z1), MARK(0)) [1] MARK(U11(tt, z1)) -> c19(A__U11(tt, z1), MARK(tt)) [1] MARK(U11(s(z016), z1)) -> c19(A__U11(s(mark(z016)), z1), MARK(s(z016))) [1] MARK(U11(nil, z1)) -> c19(A__U11(nil, z1), MARK(nil)) [1] MARK(U11(z0, z1)) -> c19(A__U11(null_mark, z1), MARK(z0)) [1] MARK(U12(zeros, z1)) -> c20(A__U12(a__zeros, z1), MARK(zeros)) [1] MARK(U12(U11(z017, z113), z1)) -> c20(A__U12(a__U11(mark(z017), z113), z1), MARK(U11(z017, z113))) [1] MARK(U12(U12(z018, z114), z1)) -> c20(A__U12(a__U12(mark(z018), z114), z1), MARK(U12(z018, z114))) [1] MARK(U12(length(z019), z1)) -> c20(A__U12(a__length(mark(z019)), z1), MARK(length(z019))) [1] MARK(U12(U21(z020, z115, z25, z35), z1)) -> c20(A__U12(a__U21(mark(z020), z115, z25, z35), z1), MARK(U21(z020, z115, z25, z35))) [1] MARK(U12(U22(z021, z116, z26, z36), z1)) -> c20(A__U12(a__U22(mark(z021), z116, z26, z36), z1), MARK(U22(z021, z116, z26, z36))) [1] MARK(U12(U23(z022, z117, z27, z37), z1)) -> c20(A__U12(a__U23(mark(z022), z117, z27, z37), z1), MARK(U23(z022, z117, z27, z37))) [1] MARK(U12(take(z023, z118), z1)) -> c20(A__U12(a__take(mark(z023), mark(z118)), z1), MARK(take(z023, z118))) [1] MARK(U12(cons(z024, z119), z1)) -> c20(A__U12(cons(mark(z024), z119), z1), MARK(cons(z024, z119))) [1] MARK(U12(0, z1)) -> c20(A__U12(0, z1), MARK(0)) [1] MARK(U12(tt, z1)) -> c20(A__U12(tt, z1), MARK(tt)) [1] MARK(U12(s(z025), z1)) -> c20(A__U12(s(mark(z025)), z1), MARK(s(z025))) [1] MARK(U12(nil, z1)) -> c20(A__U12(nil, z1), MARK(nil)) [1] MARK(U12(z0, z1)) -> c20(A__U12(null_mark, z1), MARK(z0)) [1] MARK(length(zeros)) -> c21(A__LENGTH(a__zeros), MARK(zeros)) [1] MARK(length(U11(z026, z120))) -> c21(A__LENGTH(a__U11(mark(z026), z120)), MARK(U11(z026, z120))) [1] MARK(length(U12(z027, z121))) -> c21(A__LENGTH(a__U12(mark(z027), z121)), MARK(U12(z027, z121))) [1] MARK(length(length(z028))) -> c21(A__LENGTH(a__length(mark(z028))), MARK(length(z028))) [1] MARK(length(U21(z029, z122, z28, z38))) -> c21(A__LENGTH(a__U21(mark(z029), z122, z28, z38)), MARK(U21(z029, z122, z28, z38))) [1] MARK(length(U22(z030, z123, z29, z39))) -> c21(A__LENGTH(a__U22(mark(z030), z123, z29, z39)), MARK(U22(z030, z123, z29, z39))) [1] MARK(length(U23(z031, z124, z210, z310))) -> c21(A__LENGTH(a__U23(mark(z031), z124, z210, z310)), MARK(U23(z031, z124, z210, z310))) [1] MARK(length(take(z032, z125))) -> c21(A__LENGTH(a__take(mark(z032), mark(z125))), MARK(take(z032, z125))) [1] MARK(length(cons(z033, z126))) -> c21(A__LENGTH(cons(mark(z033), z126)), MARK(cons(z033, z126))) [1] MARK(length(0)) -> c21(A__LENGTH(0), MARK(0)) [1] MARK(length(tt)) -> c21(A__LENGTH(tt), MARK(tt)) [1] MARK(length(s(z034))) -> c21(A__LENGTH(s(mark(z034))), MARK(s(z034))) [1] MARK(length(nil)) -> c21(A__LENGTH(nil), MARK(nil)) [1] MARK(length(z0)) -> c21(A__LENGTH(null_mark), MARK(z0)) [1] MARK(U21(zeros, z1, z2, z3)) -> c22(A__U21(a__zeros, z1, z2, z3), MARK(zeros)) [1] MARK(U21(U11(z035, z127), z1, z2, z3)) -> c22(A__U21(a__U11(mark(z035), z127), z1, z2, z3), MARK(U11(z035, z127))) [1] MARK(U21(U12(z036, z128), z1, z2, z3)) -> c22(A__U21(a__U12(mark(z036), z128), z1, z2, z3), MARK(U12(z036, z128))) [1] MARK(U21(length(z037), z1, z2, z3)) -> c22(A__U21(a__length(mark(z037)), z1, z2, z3), MARK(length(z037))) [1] MARK(U21(U21(z038, z129, z211, z311), z1, z2, z3)) -> c22(A__U21(a__U21(mark(z038), z129, z211, z311), z1, z2, z3), MARK(U21(z038, z129, z211, z311))) [1] MARK(U21(U22(z039, z130, z212, z312), z1, z2, z3)) -> c22(A__U21(a__U22(mark(z039), z130, z212, z312), z1, z2, z3), MARK(U22(z039, z130, z212, z312))) [1] MARK(U21(U23(z040, z131, z213, z313), z1, z2, z3)) -> c22(A__U21(a__U23(mark(z040), z131, z213, z313), z1, z2, z3), MARK(U23(z040, z131, z213, z313))) [1] MARK(U21(take(z041, z132), z1, z2, z3)) -> c22(A__U21(a__take(mark(z041), mark(z132)), z1, z2, z3), MARK(take(z041, z132))) [1] MARK(U21(cons(z042, z133), z1, z2, z3)) -> c22(A__U21(cons(mark(z042), z133), z1, z2, z3), MARK(cons(z042, z133))) [1] MARK(U21(0, z1, z2, z3)) -> c22(A__U21(0, z1, z2, z3), MARK(0)) [1] MARK(U21(tt, z1, z2, z3)) -> c22(A__U21(tt, z1, z2, z3), MARK(tt)) [1] MARK(U21(s(z043), z1, z2, z3)) -> c22(A__U21(s(mark(z043)), z1, z2, z3), MARK(s(z043))) [1] MARK(U21(nil, z1, z2, z3)) -> c22(A__U21(nil, z1, z2, z3), MARK(nil)) [1] MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(null_mark, z1, z2, z3), MARK(z0)) [1] MARK(U22(zeros, z1, z2, z3)) -> c23(A__U22(a__zeros, z1, z2, z3), MARK(zeros)) [1] MARK(U22(U11(z044, z134), z1, z2, z3)) -> c23(A__U22(a__U11(mark(z044), z134), z1, z2, z3), MARK(U11(z044, z134))) [1] MARK(U22(U12(z045, z135), z1, z2, z3)) -> c23(A__U22(a__U12(mark(z045), z135), z1, z2, z3), MARK(U12(z045, z135))) [1] MARK(U22(length(z046), z1, z2, z3)) -> c23(A__U22(a__length(mark(z046)), z1, z2, z3), MARK(length(z046))) [1] MARK(U22(U21(z047, z136, z214, z314), z1, z2, z3)) -> c23(A__U22(a__U21(mark(z047), z136, z214, z314), z1, z2, z3), MARK(U21(z047, z136, z214, z314))) [1] MARK(U22(U22(z048, z137, z215, z315), z1, z2, z3)) -> c23(A__U22(a__U22(mark(z048), z137, z215, z315), z1, z2, z3), MARK(U22(z048, z137, z215, z315))) [1] MARK(U22(U23(z049, z138, z216, z316), z1, z2, z3)) -> c23(A__U22(a__U23(mark(z049), z138, z216, z316), z1, z2, z3), MARK(U23(z049, z138, z216, z316))) [1] MARK(U22(take(z050, z139), z1, z2, z3)) -> c23(A__U22(a__take(mark(z050), mark(z139)), z1, z2, z3), MARK(take(z050, z139))) [1] MARK(U22(cons(z051, z140), z1, z2, z3)) -> c23(A__U22(cons(mark(z051), z140), z1, z2, z3), MARK(cons(z051, z140))) [1] MARK(U22(0, z1, z2, z3)) -> c23(A__U22(0, z1, z2, z3), MARK(0)) [1] MARK(U22(tt, z1, z2, z3)) -> c23(A__U22(tt, z1, z2, z3), MARK(tt)) [1] MARK(U22(s(z052), z1, z2, z3)) -> c23(A__U22(s(mark(z052)), z1, z2, z3), MARK(s(z052))) [1] MARK(U22(nil, z1, z2, z3)) -> c23(A__U22(nil, z1, z2, z3), MARK(nil)) [1] MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(null_mark, z1, z2, z3), MARK(z0)) [1] MARK(U23(zeros, z1, z2, z3)) -> c24(A__U23(a__zeros, z1, z2, z3), MARK(zeros)) [1] MARK(U23(U11(z053, z141), z1, z2, z3)) -> c24(A__U23(a__U11(mark(z053), z141), z1, z2, z3), MARK(U11(z053, z141))) [1] MARK(U23(U12(z054, z142), z1, z2, z3)) -> c24(A__U23(a__U12(mark(z054), z142), z1, z2, z3), MARK(U12(z054, z142))) [1] MARK(U23(length(z055), z1, z2, z3)) -> c24(A__U23(a__length(mark(z055)), z1, z2, z3), MARK(length(z055))) [1] MARK(U23(U21(z056, z143, z217, z317), z1, z2, z3)) -> c24(A__U23(a__U21(mark(z056), z143, z217, z317), z1, z2, z3), MARK(U21(z056, z143, z217, z317))) [1] MARK(U23(U22(z057, z144, z218, z318), z1, z2, z3)) -> c24(A__U23(a__U22(mark(z057), z144, z218, z318), z1, z2, z3), MARK(U22(z057, z144, z218, z318))) [1] MARK(U23(U23(z058, z145, z219, z319), z1, z2, z3)) -> c24(A__U23(a__U23(mark(z058), z145, z219, z319), z1, z2, z3), MARK(U23(z058, z145, z219, z319))) [1] MARK(U23(take(z059, z146), z1, z2, z3)) -> c24(A__U23(a__take(mark(z059), mark(z146)), z1, z2, z3), MARK(take(z059, z146))) [1] MARK(U23(cons(z060, z147), z1, z2, z3)) -> c24(A__U23(cons(mark(z060), z147), z1, z2, z3), MARK(cons(z060, z147))) [1] MARK(U23(0, z1, z2, z3)) -> c24(A__U23(0, z1, z2, z3), MARK(0)) [1] MARK(U23(tt, z1, z2, z3)) -> c24(A__U23(tt, z1, z2, z3), MARK(tt)) [1] MARK(U23(s(z061), z1, z2, z3)) -> c24(A__U23(s(mark(z061)), z1, z2, z3), MARK(s(z061))) [1] MARK(U23(nil, z1, z2, z3)) -> c24(A__U23(nil, z1, z2, z3), MARK(nil)) [1] MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(null_mark, z1, z2, z3), MARK(z0)) [1] MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c27(MARK(z0)) [1] MARK(s(z0)) -> c30(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__U11(tt, z0) -> a__U12(tt, z0) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U12(tt, zeros) -> s(a__length(a__zeros)) [0] a__U12(tt, U11(z0332, z1258)) -> s(a__length(a__U11(mark(z0332), z1258))) [0] a__U12(tt, U12(z0333, z1259)) -> s(a__length(a__U12(mark(z0333), z1259))) [0] a__U12(tt, length(z0334)) -> s(a__length(a__length(mark(z0334)))) [0] a__U12(tt, U21(z0335, z1260, z2110, z3110)) -> s(a__length(a__U21(mark(z0335), z1260, z2110, z3110))) [0] a__U12(tt, U22(z0336, z1261, z2111, z3111)) -> s(a__length(a__U22(mark(z0336), z1261, z2111, z3111))) [0] a__U12(tt, U23(z0337, z1262, z2112, z3112)) -> s(a__length(a__U23(mark(z0337), z1262, z2112, z3112))) [0] a__U12(tt, take(z0338, z1263)) -> s(a__length(a__take(mark(z0338), mark(z1263)))) [0] a__U12(tt, cons(z0339, z1264)) -> s(a__length(cons(mark(z0339), z1264))) [0] a__U12(tt, 0) -> s(a__length(0)) [0] a__U12(tt, tt) -> s(a__length(tt)) [0] a__U12(tt, s(z0340)) -> s(a__length(s(mark(z0340)))) [0] a__U12(tt, nil) -> s(a__length(nil)) [0] a__U12(tt, z0) -> s(a__length(null_mark)) [0] a__U12(z0, z1) -> U12(z0, z1) [0] a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) [0] a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) [0] a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) [0] a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) [0] a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) [0] a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) [0] a__length(nil) -> 0 [0] a__length(cons(z0, z1)) -> a__U11(tt, z1) [0] a__length(z0) -> length(z0) [0] a__take(0, z0) -> nil [0] a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) [0] a__take(z0, z1) -> take(z0, z1) [0] mark(zeros) -> a__zeros [0] mark(U11(zeros, z1)) -> a__U11(a__zeros, z1) [0] mark(U11(U11(z0341, z1265), z1)) -> a__U11(a__U11(mark(z0341), z1265), z1) [0] mark(U11(U12(z0342, z1266), z1)) -> a__U11(a__U12(mark(z0342), z1266), z1) [0] mark(U11(length(z0343), z1)) -> a__U11(a__length(mark(z0343)), z1) [0] mark(U11(U21(z0344, z1267, z2113, z3113), z1)) -> a__U11(a__U21(mark(z0344), z1267, z2113, z3113), z1) [0] mark(U11(U22(z0345, z1268, z2114, z3114), z1)) -> a__U11(a__U22(mark(z0345), z1268, z2114, z3114), z1) [0] mark(U11(U23(z0346, z1269, z2115, z3115), z1)) -> a__U11(a__U23(mark(z0346), z1269, z2115, z3115), z1) [0] mark(U11(take(z0347, z1270), z1)) -> a__U11(a__take(mark(z0347), mark(z1270)), z1) [0] mark(U11(cons(z0348, z1271), z1)) -> a__U11(cons(mark(z0348), z1271), z1) [0] mark(U11(0, z1)) -> a__U11(0, z1) [0] mark(U11(tt, z1)) -> a__U11(tt, z1) [0] mark(U11(s(z0349), z1)) -> a__U11(s(mark(z0349)), z1) [0] mark(U11(nil, z1)) -> a__U11(nil, z1) [0] mark(U11(z0, z1)) -> a__U11(null_mark, z1) [0] mark(U12(zeros, z1)) -> a__U12(a__zeros, z1) [0] mark(U12(U11(z0350, z1272), z1)) -> a__U12(a__U11(mark(z0350), z1272), z1) [0] mark(U12(U12(z0351, z1273), z1)) -> a__U12(a__U12(mark(z0351), z1273), z1) [0] mark(U12(length(z0352), z1)) -> a__U12(a__length(mark(z0352)), z1) [0] mark(U12(U21(z0353, z1274, z2116, z3116), z1)) -> a__U12(a__U21(mark(z0353), z1274, z2116, z3116), z1) [0] mark(U12(U22(z0354, z1275, z2117, z3117), z1)) -> a__U12(a__U22(mark(z0354), z1275, z2117, z3117), z1) [0] mark(U12(U23(z0355, z1276, z2118, z3118), z1)) -> a__U12(a__U23(mark(z0355), z1276, z2118, z3118), z1) [0] mark(U12(take(z0356, z1277), z1)) -> a__U12(a__take(mark(z0356), mark(z1277)), z1) [0] mark(U12(cons(z0357, z1278), z1)) -> a__U12(cons(mark(z0357), z1278), z1) [0] mark(U12(0, z1)) -> a__U12(0, z1) [0] mark(U12(tt, z1)) -> a__U12(tt, z1) [0] mark(U12(s(z0358), z1)) -> a__U12(s(mark(z0358)), z1) [0] mark(U12(nil, z1)) -> a__U12(nil, z1) [0] mark(U12(z0, z1)) -> a__U12(null_mark, z1) [0] mark(length(zeros)) -> a__length(a__zeros) [0] mark(length(U11(z0359, z1279))) -> a__length(a__U11(mark(z0359), z1279)) [0] mark(length(U12(z0360, z1280))) -> a__length(a__U12(mark(z0360), z1280)) [0] mark(length(length(z0361))) -> a__length(a__length(mark(z0361))) [0] mark(length(U21(z0362, z1281, z2119, z3119))) -> a__length(a__U21(mark(z0362), z1281, z2119, z3119)) [0] mark(length(U22(z0363, z1282, z2120, z3120))) -> a__length(a__U22(mark(z0363), z1282, z2120, z3120)) [0] mark(length(U23(z0364, z1283, z2121, z3121))) -> a__length(a__U23(mark(z0364), z1283, z2121, z3121)) [0] mark(length(take(z0365, z1284))) -> a__length(a__take(mark(z0365), mark(z1284))) [0] mark(length(cons(z0366, z1285))) -> a__length(cons(mark(z0366), z1285)) [0] mark(length(0)) -> a__length(0) [0] mark(length(tt)) -> a__length(tt) [0] mark(length(s(z0367))) -> a__length(s(mark(z0367))) [0] mark(length(nil)) -> a__length(nil) [0] mark(length(z0)) -> a__length(null_mark) [0] mark(U21(zeros, z1, z2, z3)) -> a__U21(a__zeros, z1, z2, z3) [0] mark(U21(U11(z0368, z1286), z1, z2, z3)) -> a__U21(a__U11(mark(z0368), z1286), z1, z2, z3) [0] mark(U21(U12(z0369, z1287), z1, z2, z3)) -> a__U21(a__U12(mark(z0369), z1287), z1, z2, z3) [0] mark(U21(length(z0370), z1, z2, z3)) -> a__U21(a__length(mark(z0370)), z1, z2, z3) [0] mark(U21(U21(z0371, z1288, z2122, z3122), z1, z2, z3)) -> a__U21(a__U21(mark(z0371), z1288, z2122, z3122), z1, z2, z3) [0] mark(U21(U22(z0372, z1289, z2123, z3123), z1, z2, z3)) -> a__U21(a__U22(mark(z0372), z1289, z2123, z3123), z1, z2, z3) [0] mark(U21(U23(z0373, z1290, z2124, z3124), z1, z2, z3)) -> a__U21(a__U23(mark(z0373), z1290, z2124, z3124), z1, z2, z3) [0] mark(U21(take(z0374, z1291), z1, z2, z3)) -> a__U21(a__take(mark(z0374), mark(z1291)), z1, z2, z3) [0] mark(U21(cons(z0375, z1292), z1, z2, z3)) -> a__U21(cons(mark(z0375), z1292), z1, z2, z3) [0] mark(U21(0, z1, z2, z3)) -> a__U21(0, z1, z2, z3) [0] mark(U21(tt, z1, z2, z3)) -> a__U21(tt, z1, z2, z3) [0] mark(U21(s(z0376), z1, z2, z3)) -> a__U21(s(mark(z0376)), z1, z2, z3) [0] mark(U21(nil, z1, z2, z3)) -> a__U21(nil, z1, z2, z3) [0] mark(U21(z0, z1, z2, z3)) -> a__U21(null_mark, z1, z2, z3) [0] mark(U22(zeros, z1, z2, z3)) -> a__U22(a__zeros, z1, z2, z3) [0] mark(U22(U11(z0377, z1293), z1, z2, z3)) -> a__U22(a__U11(mark(z0377), z1293), z1, z2, z3) [0] mark(U22(U12(z0378, z1294), z1, z2, z3)) -> a__U22(a__U12(mark(z0378), z1294), z1, z2, z3) [0] mark(U22(length(z0379), z1, z2, z3)) -> a__U22(a__length(mark(z0379)), z1, z2, z3) [0] mark(U22(U21(z0380, z1295, z2125, z3125), z1, z2, z3)) -> a__U22(a__U21(mark(z0380), z1295, z2125, z3125), z1, z2, z3) [0] mark(U22(U22(z0381, z1296, z2126, z3126), z1, z2, z3)) -> a__U22(a__U22(mark(z0381), z1296, z2126, z3126), z1, z2, z3) [0] mark(U22(U23(z0382, z1297, z2127, z3127), z1, z2, z3)) -> a__U22(a__U23(mark(z0382), z1297, z2127, z3127), z1, z2, z3) [0] mark(U22(take(z0383, z1298), z1, z2, z3)) -> a__U22(a__take(mark(z0383), mark(z1298)), z1, z2, z3) [0] mark(U22(cons(z0384, z1299), z1, z2, z3)) -> a__U22(cons(mark(z0384), z1299), z1, z2, z3) [0] mark(U22(0, z1, z2, z3)) -> a__U22(0, z1, z2, z3) [0] mark(U22(tt, z1, z2, z3)) -> a__U22(tt, z1, z2, z3) [0] mark(U22(s(z0385), z1, z2, z3)) -> a__U22(s(mark(z0385)), z1, z2, z3) [0] mark(U22(nil, z1, z2, z3)) -> a__U22(nil, z1, z2, z3) [0] mark(U22(z0, z1, z2, z3)) -> a__U22(null_mark, z1, z2, z3) [0] mark(U23(zeros, z1, z2, z3)) -> a__U23(a__zeros, z1, z2, z3) [0] mark(U23(U11(z0386, z1300), z1, z2, z3)) -> a__U23(a__U11(mark(z0386), z1300), z1, z2, z3) [0] mark(U23(U12(z0387, z1301), z1, z2, z3)) -> a__U23(a__U12(mark(z0387), z1301), z1, z2, z3) [0] mark(U23(length(z0388), z1, z2, z3)) -> a__U23(a__length(mark(z0388)), z1, z2, z3) [0] mark(U23(U21(z0389, z1302, z2128, z3128), z1, z2, z3)) -> a__U23(a__U21(mark(z0389), z1302, z2128, z3128), z1, z2, z3) [0] mark(U23(U22(z0390, z1303, z2129, z3129), z1, z2, z3)) -> a__U23(a__U22(mark(z0390), z1303, z2129, z3129), z1, z2, z3) [0] mark(U23(U23(z0391, z1304, z2130, z3130), z1, z2, z3)) -> a__U23(a__U23(mark(z0391), z1304, z2130, z3130), z1, z2, z3) [0] mark(U23(take(z0392, z1305), z1, z2, z3)) -> a__U23(a__take(mark(z0392), mark(z1305)), z1, z2, z3) [0] mark(U23(cons(z0393, z1306), z1, z2, z3)) -> a__U23(cons(mark(z0393), z1306), z1, z2, z3) [0] mark(U23(0, z1, z2, z3)) -> a__U23(0, z1, z2, z3) [0] mark(U23(tt, z1, z2, z3)) -> a__U23(tt, z1, z2, z3) [0] mark(U23(s(z0394), z1, z2, z3)) -> a__U23(s(mark(z0394)), z1, z2, z3) [0] mark(U23(nil, z1, z2, z3)) -> a__U23(nil, z1, z2, z3) [0] mark(U23(z0, z1, z2, z3)) -> a__U23(null_mark, z1, z2, z3) [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(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] a__zeros -> null_a__zeros [0] a__U11(v0, v1) -> null_a__U11 [0] a__U12(v0, v1) -> null_a__U12 [0] a__U21(v0, v1, v2, v3) -> null_a__U21 [0] a__U22(v0, v1, v2, v3) -> null_a__U22 [0] a__U23(v0, v1, v2, v3) -> null_a__U23 [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__U11 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c2 tt :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c2 :: c4 -> c2 A__U12 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c4 c4 :: c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c4 A__LENGTH :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c13 mark :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark MARK :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 A__U21 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c6 c6 :: c8 -> c6 A__U22 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c8 c8 :: c10 -> c8 A__U23 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c10 c10 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c10 cons :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c13 :: c2 -> c13 A__TAKE :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c16 s :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c16 :: c6 -> c16 U11 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c19 :: c2 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 U12 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c20 :: c4 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 length :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c21 :: c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 U21 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c22 :: c6 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 U22 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c23 :: c8 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 U23 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c24 :: c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 take :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c25 :: c16 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 c26 :: c16 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 c27 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 c30 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 a__zeros :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark 0 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark zeros :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__U11 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__U12 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__length :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__U21 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__U22 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__U23 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark nil :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__take :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__zeros :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__U11 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__U12 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__U21 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__U22 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__U23 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__length :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__take :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_mark :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark const :: c2 const1 :: c4 const2 :: c13 const3 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c30 const4 :: c6 const5 :: c8 const6 :: c10 const7 :: c16 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__U11 => 0 null_a__U12 => 0 null_a__U21 => 0 null_a__U22 => 0 null_a__U23 => 0 null_a__length => 0 null_a__take => 0 null_mark => 0 const => 0 const1 => 0 const2 => 0 const3 => 0 const4 => 0 const5 => 0 const6 => 0 const7 => 0 ---------------------------------------- (40) Obligation: Complexity RNTS consisting of the following rules: A__LENGTH(z) -{ 1 }-> 1 + A__U11(2, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAKE(z, z') -{ 1 }-> 1 + A__U21(2, z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__U11(z, z') -{ 1 }-> 1 + A__U12(2, z0) :|: z = 2, z0 >= 0, z' = z0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__zeros) + MARK(3) :|: z = 2, z' = 3 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__take(mark(z05), mark(z14))) + MARK(1 + z05 + z14) :|: z = 2, z' = 1 + z05 + z14, z05 >= 0, z14 >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__length(mark(z01))) + MARK(1 + z01) :|: z = 2, z01 >= 0, z' = 1 + z01 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__U23(mark(z04), z13, z21, z31)) + MARK(1 + z04 + z13 + z21 + z31) :|: z = 2, z04 >= 0, z21 >= 0, z31 >= 0, z' = 1 + z04 + z13 + z21 + z31, z13 >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__U22(mark(z03), z12, z2'', z3'')) + MARK(1 + z03 + z12 + z2'' + z3'') :|: z = 2, z' = 1 + z03 + z12 + z2'' + z3'', z12 >= 0, z3'' >= 0, z03 >= 0, z2'' >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__U21(mark(z02), z11, z2', z3')) + MARK(1 + z02 + z11 + z2' + z3') :|: z = 2, z' = 1 + z02 + z11 + z2' + z3', z11 >= 0, z3' >= 0, z02 >= 0, z2' >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__U12(mark(z0''), z1'')) + MARK(1 + z0'' + z1'') :|: z = 2, z0'' >= 0, z' = 1 + z0'' + z1'', z1'' >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__U11(mark(z0'), z1')) + MARK(1 + z0' + z1') :|: z = 2, z0' >= 0, z1' >= 0, z' = 1 + z0' + z1' A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(2) + MARK(2) :|: z = 2, z' = 2 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(1) + MARK(1) :|: z = 2, z' = 1 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(0) + MARK(z0) :|: z = 2, z0 >= 0, z' = z0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(0) + MARK(0) :|: z = 2, z' = 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(1 + mark(z07)) + MARK(1 + z07) :|: z = 2, z07 >= 0, z' = 1 + z07 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(1 + mark(z06) + z15) + MARK(1 + z06 + z15) :|: z = 2, z15 >= 0, z06 >= 0, z' = 1 + z06 + z15 A__U21(z, z', z'', z4) -{ 1 }-> 1 + A__U22(2, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 A__U22(z, z', z'', z4) -{ 1 }-> 1 + A__U23(2, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 A__U23(z, z', z'', z4) -{ 1 }-> 1 + MARK(z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 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__U23(a__zeros, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__take(mark(z059), mark(z146)), z1, z2, z3) + MARK(1 + z059 + z146) :|: z1 >= 0, z = 1 + (1 + z059 + z146) + z1 + z2 + z3, z059 >= 0, z2 >= 0, z3 >= 0, z146 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__length(mark(z055)), z1, z2, z3) + MARK(1 + z055) :|: z1 >= 0, z055 >= 0, z = 1 + (1 + z055) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__U23(mark(z058), z145, z219, z319), z1, z2, z3) + MARK(1 + z058 + z145 + z219 + z319) :|: z319 >= 0, z145 >= 0, z = 1 + (1 + z058 + z145 + z219 + z319) + z1 + z2 + z3, z1 >= 0, z219 >= 0, z058 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__U22(mark(z057), z144, z218, z318), z1, z2, z3) + MARK(1 + z057 + z144 + z218 + z318) :|: z = 1 + (1 + z057 + z144 + z218 + z318) + z1 + z2 + z3, z1 >= 0, z144 >= 0, z318 >= 0, z218 >= 0, z2 >= 0, z3 >= 0, z057 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__U21(mark(z056), z143, z217, z317), z1, z2, z3) + MARK(1 + z056 + z143 + z217 + z317) :|: z056 >= 0, z1 >= 0, z217 >= 0, z143 >= 0, z317 >= 0, z = 1 + (1 + z056 + z143 + z217 + z317) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__U12(mark(z054), z142), z1, z2, z3) + MARK(1 + z054 + z142) :|: z1 >= 0, z = 1 + (1 + z054 + z142) + z1 + z2 + z3, z054 >= 0, z142 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__U11(mark(z053), z141), z1, z2, z3) + MARK(1 + z053 + z141) :|: z141 >= 0, z1 >= 0, z053 >= 0, z = 1 + (1 + z053 + z141) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(2, z1, z2, z3) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(1, z1, z2, z3) + MARK(1) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(0, z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(0, z1, z2, z3) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(1 + mark(z061), z1, z2, z3) + MARK(1 + z061) :|: z = 1 + (1 + z061) + z1 + z2 + z3, z1 >= 0, z061 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(1 + mark(z060) + z147, z1, z2, z3) + MARK(1 + z060 + z147) :|: z1 >= 0, z = 1 + (1 + z060 + z147) + z1 + z2 + z3, z147 >= 0, z060 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__zeros, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__take(mark(z050), mark(z139)), z1, z2, z3) + MARK(1 + z050 + z139) :|: z1 >= 0, z139 >= 0, z = 1 + (1 + z050 + z139) + z1 + z2 + z3, z050 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__length(mark(z046)), z1, z2, z3) + MARK(1 + z046) :|: z046 >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z = 1 + (1 + z046) + z1 + z2 + z3 MARK(z) -{ 1 }-> 1 + A__U22(a__U23(mark(z049), z138, z216, z316), z1, z2, z3) + MARK(1 + z049 + z138 + z216 + z316) :|: z216 >= 0, z1 >= 0, z049 >= 0, z138 >= 0, z316 >= 0, z = 1 + (1 + z049 + z138 + z216 + z316) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__U22(mark(z048), z137, z215, z315), z1, z2, z3) + MARK(1 + z048 + z137 + z215 + z315) :|: z315 >= 0, z = 1 + (1 + z048 + z137 + z215 + z315) + z1 + z2 + z3, z1 >= 0, z048 >= 0, z137 >= 0, z2 >= 0, z3 >= 0, z215 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__U21(mark(z047), z136, z214, z314), z1, z2, z3) + MARK(1 + z047 + z136 + z214 + z314) :|: z = 1 + (1 + z047 + z136 + z214 + z314) + z1 + z2 + z3, z1 >= 0, z214 >= 0, z2 >= 0, z3 >= 0, z047 >= 0, z136 >= 0, z314 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__U12(mark(z045), z135), z1, z2, z3) + MARK(1 + z045 + z135) :|: z1 >= 0, z045 >= 0, z = 1 + (1 + z045 + z135) + z1 + z2 + z3, z135 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__U11(mark(z044), z134), z1, z2, z3) + MARK(1 + z044 + z134) :|: z1 >= 0, z134 >= 0, z044 >= 0, z = 1 + (1 + z044 + z134) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(2, z1, z2, z3) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(1, z1, z2, z3) + MARK(1) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(0, z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(0, z1, z2, z3) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(1 + mark(z052), z1, z2, z3) + MARK(1 + z052) :|: z052 >= 0, z1 >= 0, z = 1 + (1 + z052) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(1 + mark(z051) + z140, z1, z2, z3) + MARK(1 + z051 + z140) :|: z1 >= 0, z = 1 + (1 + z051 + z140) + z1 + z2 + z3, z051 >= 0, z140 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__zeros, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__take(mark(z041), mark(z132)), z1, z2, z3) + MARK(1 + z041 + z132) :|: z1 >= 0, z = 1 + (1 + z041 + z132) + z1 + z2 + z3, z132 >= 0, z041 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__length(mark(z037)), z1, z2, z3) + MARK(1 + z037) :|: z = 1 + (1 + z037) + z1 + z2 + z3, z1 >= 0, z037 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U23(mark(z040), z131, z213, z313), z1, z2, z3) + MARK(1 + z040 + z131 + z213 + z313) :|: z131 >= 0, z1 >= 0, z213 >= 0, z040 >= 0, z313 >= 0, z = 1 + (1 + z040 + z131 + z213 + z313) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U22(mark(z039), z130, z212, z312), z1, z2, z3) + MARK(1 + z039 + z130 + z212 + z312) :|: z212 >= 0, z130 >= 0, z1 >= 0, z039 >= 0, z312 >= 0, z = 1 + (1 + z039 + z130 + z212 + z312) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U21(mark(z038), z129, z211, z311), z1, z2, z3) + MARK(1 + z038 + z129 + z211 + z311) :|: z311 >= 0, z = 1 + (1 + z038 + z129 + z211 + z311) + z1 + z2 + z3, z1 >= 0, z129 >= 0, z211 >= 0, z038 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U12(mark(z036), z128), z1, z2, z3) + MARK(1 + z036 + z128) :|: z = 1 + (1 + z036 + z128) + z1 + z2 + z3, z036 >= 0, z1 >= 0, z128 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U11(mark(z035), z127), z1, z2, z3) + MARK(1 + z035 + z127) :|: z035 >= 0, z1 >= 0, z = 1 + (1 + z035 + z127) + z1 + z2 + z3, z127 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(2, z1, z2, z3) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1, z1, z2, z3) + MARK(1) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(0, z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(0, z1, z2, z3) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1 + mark(z043), z1, z2, z3) + MARK(1 + z043) :|: z1 >= 0, z043 >= 0, z = 1 + (1 + z043) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1 + mark(z042) + z133, z1, z2, z3) + MARK(1 + z042 + z133) :|: z042 >= 0, z1 >= 0, z133 >= 0, z = 1 + (1 + z042 + z133) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__zeros, z1) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 MARK(z) -{ 1 }-> 1 + A__U12(a__take(mark(z023), mark(z118)), z1) + MARK(1 + z023 + z118) :|: z1 >= 0, z118 >= 0, z = 1 + (1 + z023 + z118) + z1, z023 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__length(mark(z019)), z1) + MARK(1 + z019) :|: z019 >= 0, z1 >= 0, z = 1 + (1 + z019) + z1 MARK(z) -{ 1 }-> 1 + A__U12(a__U23(mark(z022), z117, z27, z37), z1) + MARK(1 + z022 + z117 + z27 + z37) :|: z117 >= 0, z1 >= 0, z022 >= 0, z = 1 + (1 + z022 + z117 + z27 + z37) + z1, z27 >= 0, z37 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U22(mark(z021), z116, z26, z36), z1) + MARK(1 + z021 + z116 + z26 + z36) :|: z021 >= 0, z = 1 + (1 + z021 + z116 + z26 + z36) + z1, z1 >= 0, z26 >= 0, z36 >= 0, z116 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U21(mark(z020), z115, z25, z35), z1) + MARK(1 + z020 + z115 + z25 + z35) :|: z25 >= 0, z1 >= 0, z = 1 + (1 + z020 + z115 + z25 + z35) + z1, z35 >= 0, z115 >= 0, z020 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U12(mark(z018), z114), z1) + MARK(1 + z018 + z114) :|: z114 >= 0, z1 >= 0, z = 1 + (1 + z018 + z114) + z1, z018 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U11(mark(z017), z113), z1) + MARK(1 + z017 + z113) :|: z1 >= 0, z = 1 + (1 + z017 + z113) + z1, z113 >= 0, z017 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(2, z1) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 MARK(z) -{ 1 }-> 1 + A__U12(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 MARK(z) -{ 1 }-> 1 + A__U12(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U12(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 MARK(z) -{ 1 }-> 1 + A__U12(1 + mark(z025), z1) + MARK(1 + z025) :|: z025 >= 0, z1 >= 0, z = 1 + (1 + z025) + z1 MARK(z) -{ 1 }-> 1 + A__U12(1 + mark(z024) + z119, z1) + MARK(1 + z024 + z119) :|: z1 >= 0, z024 >= 0, z = 1 + (1 + z024 + z119) + z1, z119 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__zeros, z1) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 MARK(z) -{ 1 }-> 1 + A__U11(a__take(mark(z014), mark(z111)), z1) + MARK(1 + z014 + z111) :|: z = 1 + (1 + z014 + z111) + z1, z1 >= 0, z014 >= 0, z111 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__length(mark(z010)), z1) + MARK(1 + z010) :|: z1 >= 0, z = 1 + (1 + z010) + z1, z010 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U23(mark(z013), z110, z24, z34), z1) + MARK(1 + z013 + z110 + z24 + z34) :|: z110 >= 0, z1 >= 0, z = 1 + (1 + z013 + z110 + z24 + z34) + z1, z013 >= 0, z24 >= 0, z34 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U22(mark(z012), z19, z23, z33), z1) + MARK(1 + z012 + z19 + z23 + z33) :|: z1 >= 0, z19 >= 0, z23 >= 0, z012 >= 0, z = 1 + (1 + z012 + z19 + z23 + z33) + z1, z33 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U21(mark(z011), z18, z22, z32), z1) + MARK(1 + z011 + z18 + z22 + z32) :|: z18 >= 0, z011 >= 0, z32 >= 0, z1 >= 0, z = 1 + (1 + z011 + z18 + z22 + z32) + z1, z22 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U12(mark(z09), z17), z1) + MARK(1 + z09 + z17) :|: z1 >= 0, z17 >= 0, z = 1 + (1 + z09 + z17) + z1, z09 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U11(mark(z08), z16), z1) + MARK(1 + z08 + z16) :|: z08 >= 0, z1 >= 0, z16 >= 0, z = 1 + (1 + z08 + z16) + z1 MARK(z) -{ 1 }-> 1 + A__U11(2, z1) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 MARK(z) -{ 1 }-> 1 + A__U11(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 MARK(z) -{ 1 }-> 1 + A__U11(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U11(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z016), z1) + MARK(1 + z016) :|: z1 >= 0, z016 >= 0, z = 1 + (1 + z016) + z1 MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z015) + z112, z1) + MARK(1 + z015 + z112) :|: z015 >= 0, z1 >= 0, z112 >= 0, z = 1 + (1 + z015 + z112) + z1 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(z032), mark(z125))) + MARK(1 + z032 + z125) :|: z032 >= 0, z = 1 + (1 + z032 + z125), z125 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__length(mark(z028))) + MARK(1 + z028) :|: z028 >= 0, z = 1 + (1 + z028) MARK(z) -{ 1 }-> 1 + A__LENGTH(a__U23(mark(z031), z124, z210, z310)) + MARK(1 + z031 + z124 + z210 + z310) :|: z031 >= 0, z124 >= 0, z310 >= 0, z210 >= 0, z = 1 + (1 + z031 + z124 + z210 + z310) MARK(z) -{ 1 }-> 1 + A__LENGTH(a__U22(mark(z030), z123, z29, z39)) + MARK(1 + z030 + z123 + z29 + z39) :|: z = 1 + (1 + z030 + z123 + z29 + z39), z29 >= 0, z39 >= 0, z123 >= 0, z030 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__U21(mark(z029), z122, z28, z38)) + MARK(1 + z029 + z122 + z28 + z38) :|: z029 >= 0, z = 1 + (1 + z029 + z122 + z28 + z38), z28 >= 0, z38 >= 0, z122 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__U12(mark(z027), z121)) + MARK(1 + z027 + z121) :|: z = 1 + (1 + z027 + z121), z121 >= 0, z027 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__U11(mark(z026), z120)) + MARK(1 + z026 + z120) :|: z120 >= 0, z = 1 + (1 + z026 + z120), z026 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__LENGTH(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z034)) + MARK(1 + z034) :|: z034 >= 0, z = 1 + (1 + z034) MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z033) + z126) + MARK(1 + z033 + z126) :|: z = 1 + (1 + z033 + z126), z033 >= 0, z126 >= 0 a__U11(z, z') -{ 0 }-> a__U12(2, z0) :|: z = 2, z0 >= 0, z' = z0 a__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U11(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U12(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U12(z, z') -{ 0 }-> 1 + a__length(a__zeros) :|: z = 2, z' = 3 a__U12(z, z') -{ 0 }-> 1 + a__length(a__take(mark(z0338), mark(z1263))) :|: z = 2, z0338 >= 0, z1263 >= 0, z' = 1 + z0338 + z1263 a__U12(z, z') -{ 0 }-> 1 + a__length(a__length(mark(z0334))) :|: z = 2, z0334 >= 0, z' = 1 + z0334 a__U12(z, z') -{ 0 }-> 1 + a__length(a__U23(mark(z0337), z1262, z2112, z3112)) :|: z = 2, z3112 >= 0, z0337 >= 0, z1262 >= 0, z' = 1 + z0337 + z1262 + z2112 + z3112, z2112 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(a__U22(mark(z0336), z1261, z2111, z3111)) :|: z = 2, z2111 >= 0, z' = 1 + z0336 + z1261 + z2111 + z3111, z1261 >= 0, z3111 >= 0, z0336 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(a__U21(mark(z0335), z1260, z2110, z3110)) :|: z = 2, z' = 1 + z0335 + z1260 + z2110 + z3110, z2110 >= 0, z0335 >= 0, z3110 >= 0, z1260 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(a__U12(mark(z0333), z1259)) :|: z = 2, z' = 1 + z0333 + z1259, z1259 >= 0, z0333 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(a__U11(mark(z0332), z1258)) :|: z = 2, z1258 >= 0, z' = 1 + z0332 + z1258, z0332 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(2) :|: z = 2, z' = 2 a__U12(z, z') -{ 0 }-> 1 + a__length(1) :|: z = 2, z' = 1 a__U12(z, z') -{ 0 }-> 1 + a__length(0) :|: z = 2, z' = 0 a__U12(z, z') -{ 0 }-> 1 + a__length(0) :|: z = 2, z0 >= 0, z' = z0 a__U12(z, z') -{ 0 }-> 1 + a__length(1 + mark(z0340)) :|: z = 2, z' = 1 + z0340, z0340 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(1 + mark(z0339) + z1264) :|: z = 2, z' = 1 + z0339 + z1264, z1264 >= 0, z0339 >= 0 a__U12(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U21(z, z', z'', z4) -{ 0 }-> a__U22(2, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U21(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U21(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__U22(z, z', z'', z4) -{ 0 }-> a__U23(2, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U22(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U22(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__U23(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U23(z, z', z'', z4) -{ 0 }-> 1 + mark(z2) + (1 + z1 + z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U23(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__length(z) -{ 0 }-> a__U11(2, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 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__take(z, z') -{ 0 }-> a__U21(2, z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 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__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(z0365), mark(z1284))) :|: z = 1 + (1 + z0365 + z1284), z0365 >= 0, z1284 >= 0 mark(z) -{ 0 }-> a__length(a__length(mark(z0361))) :|: z0361 >= 0, z = 1 + (1 + z0361) mark(z) -{ 0 }-> a__length(a__U23(mark(z0364), z1283, z2121, z3121)) :|: z2121 >= 0, z1283 >= 0, z = 1 + (1 + z0364 + z1283 + z2121 + z3121), z3121 >= 0, z0364 >= 0 mark(z) -{ 0 }-> a__length(a__U22(mark(z0363), z1282, z2120, z3120)) :|: z = 1 + (1 + z0363 + z1282 + z2120 + z3120), z1282 >= 0, z3120 >= 0, z2120 >= 0, z0363 >= 0 mark(z) -{ 0 }-> a__length(a__U21(mark(z0362), z1281, z2119, z3119)) :|: z2119 >= 0, z1281 >= 0, z3119 >= 0, z = 1 + (1 + z0362 + z1281 + z2119 + z3119), z0362 >= 0 mark(z) -{ 0 }-> a__length(a__U12(mark(z0360), z1280)) :|: z = 1 + (1 + z0360 + z1280), z0360 >= 0, z1280 >= 0 mark(z) -{ 0 }-> a__length(a__U11(mark(z0359), z1279)) :|: z = 1 + (1 + z0359 + z1279), z0359 >= 0, z1279 >= 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(z0367)) :|: z = 1 + (1 + z0367), z0367 >= 0 mark(z) -{ 0 }-> a__length(1 + mark(z0366) + z1285) :|: z1285 >= 0, z0366 >= 0, z = 1 + (1 + z0366 + z1285) mark(z) -{ 0 }-> a__U23(a__zeros, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__take(mark(z0392), mark(z1305)), z1, z2, z3) :|: z1305 >= 0, z1 >= 0, z0392 >= 0, z = 1 + (1 + z0392 + z1305) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__length(mark(z0388)), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0388) + z1 + z2 + z3, z0388 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__U23(mark(z0391), z1304, z2130, z3130), z1, z2, z3) :|: z3130 >= 0, z1304 >= 0, z1 >= 0, z = 1 + (1 + z0391 + z1304 + z2130 + z3130) + z1 + z2 + z3, z2130 >= 0, z0391 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__U22(mark(z0390), z1303, z2129, z3129), z1, z2, z3) :|: z2129 >= 0, z1 >= 0, z = 1 + (1 + z0390 + z1303 + z2129 + z3129) + z1 + z2 + z3, z0390 >= 0, z1303 >= 0, z3129 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__U21(mark(z0389), z1302, z2128, z3128), z1, z2, z3) :|: z3128 >= 0, z1 >= 0, z1302 >= 0, z2128 >= 0, z = 1 + (1 + z0389 + z1302 + z2128 + z3128) + z1 + z2 + z3, z0389 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__U12(mark(z0387), z1301), z1, z2, z3) :|: z1301 >= 0, z1 >= 0, z0387 >= 0, z = 1 + (1 + z0387 + z1301) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__U11(mark(z0386), z1300), z1, z2, z3) :|: z = 1 + (1 + z0386 + z1300) + z1 + z2 + z3, z0386 >= 0, z1300 >= 0, z1 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(2, z1, z2, z3) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(1, z1, z2, z3) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(0, z1, z2, z3) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(0, z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(1 + mark(z0394), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0394) + z1 + z2 + z3, z0394 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(1 + mark(z0393) + z1306, z1, z2, z3) :|: z = 1 + (1 + z0393 + z1306) + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0, z0393 >= 0, z1306 >= 0 mark(z) -{ 0 }-> a__U22(a__zeros, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(a__take(mark(z0383), mark(z1298)), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0383 + z1298) + z1 + z2 + z3, z1298 >= 0, z2 >= 0, z3 >= 0, z0383 >= 0 mark(z) -{ 0 }-> a__U22(a__length(mark(z0379)), z1, z2, z3) :|: z = 1 + (1 + z0379) + z1 + z2 + z3, z1 >= 0, z0379 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(a__U23(mark(z0382), z1297, z2127, z3127), z1, z2, z3) :|: z0382 >= 0, z1 >= 0, z2127 >= 0, z = 1 + (1 + z0382 + z1297 + z2127 + z3127) + z1 + z2 + z3, z3127 >= 0, z2 >= 0, z3 >= 0, z1297 >= 0 mark(z) -{ 0 }-> a__U22(a__U22(mark(z0381), z1296, z2126, z3126), z1, z2, z3) :|: z1296 >= 0, z2126 >= 0, z1 >= 0, z = 1 + (1 + z0381 + z1296 + z2126 + z3126) + z1 + z2 + z3, z0381 >= 0, z3126 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(a__U21(mark(z0380), z1295, z2125, z3125), z1, z2, z3) :|: z2125 >= 0, z1 >= 0, z1295 >= 0, z0380 >= 0, z3125 >= 0, z = 1 + (1 + z0380 + z1295 + z2125 + z3125) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(a__U12(mark(z0378), z1294), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0378 + z1294) + z1 + z2 + z3, z0378 >= 0, z1294 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(a__U11(mark(z0377), z1293), z1, z2, z3) :|: z1 >= 0, z0377 >= 0, z1293 >= 0, z = 1 + (1 + z0377 + z1293) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(2, z1, z2, z3) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(1, z1, z2, z3) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(0, z1, z2, z3) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(0, z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(1 + mark(z0385), z1, z2, z3) :|: z1 >= 0, z0385 >= 0, z = 1 + (1 + z0385) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(1 + mark(z0384) + z1299, z1, z2, z3) :|: z1 >= 0, z1299 >= 0, z0384 >= 0, z = 1 + (1 + z0384 + z1299) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(a__zeros, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(a__take(mark(z0374), mark(z1291)), z1, z2, z3) :|: z1 >= 0, z1291 >= 0, z = 1 + (1 + z0374 + z1291) + z1 + z2 + z3, z0374 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(a__length(mark(z0370)), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0370) + z1 + z2 + z3, z0370 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(a__U23(mark(z0373), z1290, z2124, z3124), z1, z2, z3) :|: z = 1 + (1 + z0373 + z1290 + z2124 + z3124) + z1 + z2 + z3, z3124 >= 0, z1 >= 0, z1290 >= 0, z2124 >= 0, z2 >= 0, z3 >= 0, z0373 >= 0 mark(z) -{ 0 }-> a__U21(a__U22(mark(z0372), z1289, z2123, z3123), z1, z2, z3) :|: z0372 >= 0, z1 >= 0, z1289 >= 0, z3123 >= 0, z = 1 + (1 + z0372 + z1289 + z2123 + z3123) + z1 + z2 + z3, z2123 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(a__U21(mark(z0371), z1288, z2122, z3122), z1, z2, z3) :|: z2122 >= 0, z1 >= 0, z0371 >= 0, z3122 >= 0, z = 1 + (1 + z0371 + z1288 + z2122 + z3122) + z1 + z2 + z3, z1288 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(a__U12(mark(z0369), z1287), z1, z2, z3) :|: z1 >= 0, z0369 >= 0, z = 1 + (1 + z0369 + z1287) + z1 + z2 + z3, z2 >= 0, z3 >= 0, z1287 >= 0 mark(z) -{ 0 }-> a__U21(a__U11(mark(z0368), z1286), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0368 + z1286) + z1 + z2 + z3, z0368 >= 0, z1286 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(2, z1, z2, z3) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(1, z1, z2, z3) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(0, z1, z2, z3) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(0, z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(1 + mark(z0376), z1, z2, z3) :|: z0376 >= 0, z1 >= 0, z = 1 + (1 + z0376) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(1 + mark(z0375) + z1292, z1, z2, z3) :|: z1292 >= 0, z = 1 + (1 + z0375 + z1292) + z1 + z2 + z3, z1 >= 0, z0375 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U12(a__zeros, z1) :|: z1 >= 0, z = 1 + 3 + z1 mark(z) -{ 0 }-> a__U12(a__take(mark(z0356), mark(z1277)), z1) :|: z1 >= 0, z = 1 + (1 + z0356 + z1277) + z1, z0356 >= 0, z1277 >= 0 mark(z) -{ 0 }-> a__U12(a__length(mark(z0352)), z1) :|: z1 >= 0, z = 1 + (1 + z0352) + z1, z0352 >= 0 mark(z) -{ 0 }-> a__U12(a__U23(mark(z0355), z1276, z2118, z3118), z1) :|: z = 1 + (1 + z0355 + z1276 + z2118 + z3118) + z1, z1 >= 0, z0355 >= 0, z2118 >= 0, z3118 >= 0, z1276 >= 0 mark(z) -{ 0 }-> a__U12(a__U22(mark(z0354), z1275, z2117, z3117), z1) :|: z3117 >= 0, z1 >= 0, z1275 >= 0, z = 1 + (1 + z0354 + z1275 + z2117 + z3117) + z1, z2117 >= 0, z0354 >= 0 mark(z) -{ 0 }-> a__U12(a__U21(mark(z0353), z1274, z2116, z3116), z1) :|: z1 >= 0, z2116 >= 0, z1274 >= 0, z = 1 + (1 + z0353 + z1274 + z2116 + z3116) + z1, z3116 >= 0, z0353 >= 0 mark(z) -{ 0 }-> a__U12(a__U12(mark(z0351), z1273), z1) :|: z1 >= 0, z = 1 + (1 + z0351 + z1273) + z1, z0351 >= 0, z1273 >= 0 mark(z) -{ 0 }-> a__U12(a__U11(mark(z0350), z1272), z1) :|: z1 >= 0, z0350 >= 0, z1272 >= 0, z = 1 + (1 + z0350 + z1272) + z1 mark(z) -{ 0 }-> a__U12(2, z1) :|: z1 >= 0, z = 1 + 2 + z1 mark(z) -{ 0 }-> a__U12(1, z1) :|: z1 >= 0, z = 1 + 1 + z1 mark(z) -{ 0 }-> a__U12(0, z1) :|: z1 >= 0, z = 1 + 0 + z1 mark(z) -{ 0 }-> a__U12(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U12(1 + mark(z0358), z1) :|: z1 >= 0, z = 1 + (1 + z0358) + z1, z0358 >= 0 mark(z) -{ 0 }-> a__U12(1 + mark(z0357) + z1278, z1) :|: z = 1 + (1 + z0357 + z1278) + z1, z1 >= 0, z0357 >= 0, z1278 >= 0 mark(z) -{ 0 }-> a__U11(a__zeros, z1) :|: z1 >= 0, z = 1 + 3 + z1 mark(z) -{ 0 }-> a__U11(a__take(mark(z0347), mark(z1270)), z1) :|: z1 >= 0, z0347 >= 0, z1270 >= 0, z = 1 + (1 + z0347 + z1270) + z1 mark(z) -{ 0 }-> a__U11(a__length(mark(z0343)), z1) :|: z1 >= 0, z = 1 + (1 + z0343) + z1, z0343 >= 0 mark(z) -{ 0 }-> a__U11(a__U23(mark(z0346), z1269, z2115, z3115), z1) :|: z2115 >= 0, z1 >= 0, z1269 >= 0, z3115 >= 0, z0346 >= 0, z = 1 + (1 + z0346 + z1269 + z2115 + z3115) + z1 mark(z) -{ 0 }-> a__U11(a__U22(mark(z0345), z1268, z2114, z3114), z1) :|: z1268 >= 0, z1 >= 0, z0345 >= 0, z = 1 + (1 + z0345 + z1268 + z2114 + z3114) + z1, z3114 >= 0, z2114 >= 0 mark(z) -{ 0 }-> a__U11(a__U21(mark(z0344), z1267, z2113, z3113), z1) :|: z3113 >= 0, z0344 >= 0, z1 >= 0, z2113 >= 0, z = 1 + (1 + z0344 + z1267 + z2113 + z3113) + z1, z1267 >= 0 mark(z) -{ 0 }-> a__U11(a__U12(mark(z0342), z1266), z1) :|: z1 >= 0, z = 1 + (1 + z0342 + z1266) + z1, z0342 >= 0, z1266 >= 0 mark(z) -{ 0 }-> a__U11(a__U11(mark(z0341), z1265), z1) :|: z = 1 + (1 + z0341 + z1265) + z1, z0341 >= 0, z1 >= 0, z1265 >= 0 mark(z) -{ 0 }-> a__U11(2, z1) :|: z1 >= 0, z = 1 + 2 + z1 mark(z) -{ 0 }-> a__U11(1, z1) :|: z1 >= 0, z = 1 + 1 + z1 mark(z) -{ 0 }-> a__U11(0, z1) :|: z1 >= 0, z = 1 + 0 + z1 mark(z) -{ 0 }-> a__U11(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U11(1 + mark(z0349), z1) :|: z1 >= 0, z0349 >= 0, z = 1 + (1 + z0349) + z1 mark(z) -{ 0 }-> a__U11(1 + mark(z0348) + z1271, z1) :|: z1271 >= 0, z0348 >= 0, z1 >= 0, z = 1 + (1 + z0348 + z1271) + 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__LENGTH(z) -{ 1 }-> 1 + A__U11(2, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAKE(z, z') -{ 1 }-> 1 + A__U21(2, z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__U11(z, z') -{ 1 }-> 1 + A__U12(2, z0) :|: z = 2, z0 >= 0, z' = z0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__take(mark(z05), mark(z14))) + MARK(1 + z05 + z14) :|: z = 2, z' = 1 + z05 + z14, z05 >= 0, z14 >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__length(mark(z01))) + MARK(1 + z01) :|: z = 2, z01 >= 0, z' = 1 + z01 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__U23(mark(z04), z13, z21, z31)) + MARK(1 + z04 + z13 + z21 + z31) :|: z = 2, z04 >= 0, z21 >= 0, z31 >= 0, z' = 1 + z04 + z13 + z21 + z31, z13 >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__U22(mark(z03), z12, z2'', z3'')) + MARK(1 + z03 + z12 + z2'' + z3'') :|: z = 2, z' = 1 + z03 + z12 + z2'' + z3'', z12 >= 0, z3'' >= 0, z03 >= 0, z2'' >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__U21(mark(z02), z11, z2', z3')) + MARK(1 + z02 + z11 + z2' + z3') :|: z = 2, z' = 1 + z02 + z11 + z2' + z3', z11 >= 0, z3' >= 0, z02 >= 0, z2' >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__U12(mark(z0''), z1'')) + MARK(1 + z0'' + z1'') :|: z = 2, z0'' >= 0, z' = 1 + z0'' + z1'', z1'' >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__U11(mark(z0'), z1')) + MARK(1 + z0' + z1') :|: z = 2, z0' >= 0, z1' >= 0, z' = 1 + z0' + z1' A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(3) + MARK(3) :|: z = 2, z' = 3 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(2) + MARK(2) :|: z = 2, z' = 2 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(1) + MARK(1) :|: z = 2, z' = 1 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(0) + MARK(z0) :|: z = 2, z0 >= 0, z' = z0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(0) + MARK(3) :|: z = 2, z' = 3 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(0) + MARK(0) :|: z = 2, z' = 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(1 + mark(z07)) + MARK(1 + z07) :|: z = 2, z07 >= 0, z' = 1 + z07 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(1 + mark(z06) + z15) + MARK(1 + z06 + z15) :|: z = 2, z15 >= 0, z06 >= 0, z' = 1 + z06 + z15 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(1 + 0 + 3) + MARK(3) :|: z = 2, z' = 3 A__U21(z, z', z'', z4) -{ 1 }-> 1 + A__U22(2, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 A__U22(z, z', z'', z4) -{ 1 }-> 1 + A__U23(2, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 A__U23(z, z', z'', z4) -{ 1 }-> 1 + MARK(z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 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__U23(a__take(mark(z059), mark(z146)), z1, z2, z3) + MARK(1 + z059 + z146) :|: z1 >= 0, z = 1 + (1 + z059 + z146) + z1 + z2 + z3, z059 >= 0, z2 >= 0, z3 >= 0, z146 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__length(mark(z055)), z1, z2, z3) + MARK(1 + z055) :|: z1 >= 0, z055 >= 0, z = 1 + (1 + z055) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__U23(mark(z058), z145, z219, z319), z1, z2, z3) + MARK(1 + z058 + z145 + z219 + z319) :|: z319 >= 0, z145 >= 0, z = 1 + (1 + z058 + z145 + z219 + z319) + z1 + z2 + z3, z1 >= 0, z219 >= 0, z058 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__U22(mark(z057), z144, z218, z318), z1, z2, z3) + MARK(1 + z057 + z144 + z218 + z318) :|: z = 1 + (1 + z057 + z144 + z218 + z318) + z1 + z2 + z3, z1 >= 0, z144 >= 0, z318 >= 0, z218 >= 0, z2 >= 0, z3 >= 0, z057 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__U21(mark(z056), z143, z217, z317), z1, z2, z3) + MARK(1 + z056 + z143 + z217 + z317) :|: z056 >= 0, z1 >= 0, z217 >= 0, z143 >= 0, z317 >= 0, z = 1 + (1 + z056 + z143 + z217 + z317) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__U12(mark(z054), z142), z1, z2, z3) + MARK(1 + z054 + z142) :|: z1 >= 0, z = 1 + (1 + z054 + z142) + z1 + z2 + z3, z054 >= 0, z142 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__U11(mark(z053), z141), z1, z2, z3) + MARK(1 + z053 + z141) :|: z141 >= 0, z1 >= 0, z053 >= 0, z = 1 + (1 + z053 + z141) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(3, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(2, z1, z2, z3) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(1, z1, z2, z3) + MARK(1) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(0, z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(0, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(0, z1, z2, z3) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(1 + mark(z061), z1, z2, z3) + MARK(1 + z061) :|: z = 1 + (1 + z061) + z1 + z2 + z3, z1 >= 0, z061 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(1 + mark(z060) + z147, z1, z2, z3) + MARK(1 + z060 + z147) :|: z1 >= 0, z = 1 + (1 + z060 + z147) + z1 + z2 + z3, z147 >= 0, z060 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(1 + 0 + 3, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__take(mark(z050), mark(z139)), z1, z2, z3) + MARK(1 + z050 + z139) :|: z1 >= 0, z139 >= 0, z = 1 + (1 + z050 + z139) + z1 + z2 + z3, z050 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__length(mark(z046)), z1, z2, z3) + MARK(1 + z046) :|: z046 >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z = 1 + (1 + z046) + z1 + z2 + z3 MARK(z) -{ 1 }-> 1 + A__U22(a__U23(mark(z049), z138, z216, z316), z1, z2, z3) + MARK(1 + z049 + z138 + z216 + z316) :|: z216 >= 0, z1 >= 0, z049 >= 0, z138 >= 0, z316 >= 0, z = 1 + (1 + z049 + z138 + z216 + z316) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__U22(mark(z048), z137, z215, z315), z1, z2, z3) + MARK(1 + z048 + z137 + z215 + z315) :|: z315 >= 0, z = 1 + (1 + z048 + z137 + z215 + z315) + z1 + z2 + z3, z1 >= 0, z048 >= 0, z137 >= 0, z2 >= 0, z3 >= 0, z215 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__U21(mark(z047), z136, z214, z314), z1, z2, z3) + MARK(1 + z047 + z136 + z214 + z314) :|: z = 1 + (1 + z047 + z136 + z214 + z314) + z1 + z2 + z3, z1 >= 0, z214 >= 0, z2 >= 0, z3 >= 0, z047 >= 0, z136 >= 0, z314 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__U12(mark(z045), z135), z1, z2, z3) + MARK(1 + z045 + z135) :|: z1 >= 0, z045 >= 0, z = 1 + (1 + z045 + z135) + z1 + z2 + z3, z135 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__U11(mark(z044), z134), z1, z2, z3) + MARK(1 + z044 + z134) :|: z1 >= 0, z134 >= 0, z044 >= 0, z = 1 + (1 + z044 + z134) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(3, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(2, z1, z2, z3) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(1, z1, z2, z3) + MARK(1) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(0, z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(0, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(0, z1, z2, z3) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(1 + mark(z052), z1, z2, z3) + MARK(1 + z052) :|: z052 >= 0, z1 >= 0, z = 1 + (1 + z052) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(1 + mark(z051) + z140, z1, z2, z3) + MARK(1 + z051 + z140) :|: z1 >= 0, z = 1 + (1 + z051 + z140) + z1 + z2 + z3, z051 >= 0, z140 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(1 + 0 + 3, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__take(mark(z041), mark(z132)), z1, z2, z3) + MARK(1 + z041 + z132) :|: z1 >= 0, z = 1 + (1 + z041 + z132) + z1 + z2 + z3, z132 >= 0, z041 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__length(mark(z037)), z1, z2, z3) + MARK(1 + z037) :|: z = 1 + (1 + z037) + z1 + z2 + z3, z1 >= 0, z037 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U23(mark(z040), z131, z213, z313), z1, z2, z3) + MARK(1 + z040 + z131 + z213 + z313) :|: z131 >= 0, z1 >= 0, z213 >= 0, z040 >= 0, z313 >= 0, z = 1 + (1 + z040 + z131 + z213 + z313) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U22(mark(z039), z130, z212, z312), z1, z2, z3) + MARK(1 + z039 + z130 + z212 + z312) :|: z212 >= 0, z130 >= 0, z1 >= 0, z039 >= 0, z312 >= 0, z = 1 + (1 + z039 + z130 + z212 + z312) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U21(mark(z038), z129, z211, z311), z1, z2, z3) + MARK(1 + z038 + z129 + z211 + z311) :|: z311 >= 0, z = 1 + (1 + z038 + z129 + z211 + z311) + z1 + z2 + z3, z1 >= 0, z129 >= 0, z211 >= 0, z038 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U12(mark(z036), z128), z1, z2, z3) + MARK(1 + z036 + z128) :|: z = 1 + (1 + z036 + z128) + z1 + z2 + z3, z036 >= 0, z1 >= 0, z128 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U11(mark(z035), z127), z1, z2, z3) + MARK(1 + z035 + z127) :|: z035 >= 0, z1 >= 0, z = 1 + (1 + z035 + z127) + z1 + z2 + z3, z127 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(3, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(2, z1, z2, z3) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1, z1, z2, z3) + MARK(1) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(0, z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(0, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(0, z1, z2, z3) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1 + mark(z043), z1, z2, z3) + MARK(1 + z043) :|: z1 >= 0, z043 >= 0, z = 1 + (1 + z043) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1 + mark(z042) + z133, z1, z2, z3) + MARK(1 + z042 + z133) :|: z042 >= 0, z1 >= 0, z133 >= 0, z = 1 + (1 + z042 + z133) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1 + 0 + 3, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__take(mark(z023), mark(z118)), z1) + MARK(1 + z023 + z118) :|: z1 >= 0, z118 >= 0, z = 1 + (1 + z023 + z118) + z1, z023 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__length(mark(z019)), z1) + MARK(1 + z019) :|: z019 >= 0, z1 >= 0, z = 1 + (1 + z019) + z1 MARK(z) -{ 1 }-> 1 + A__U12(a__U23(mark(z022), z117, z27, z37), z1) + MARK(1 + z022 + z117 + z27 + z37) :|: z117 >= 0, z1 >= 0, z022 >= 0, z = 1 + (1 + z022 + z117 + z27 + z37) + z1, z27 >= 0, z37 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U22(mark(z021), z116, z26, z36), z1) + MARK(1 + z021 + z116 + z26 + z36) :|: z021 >= 0, z = 1 + (1 + z021 + z116 + z26 + z36) + z1, z1 >= 0, z26 >= 0, z36 >= 0, z116 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U21(mark(z020), z115, z25, z35), z1) + MARK(1 + z020 + z115 + z25 + z35) :|: z25 >= 0, z1 >= 0, z = 1 + (1 + z020 + z115 + z25 + z35) + z1, z35 >= 0, z115 >= 0, z020 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U12(mark(z018), z114), z1) + MARK(1 + z018 + z114) :|: z114 >= 0, z1 >= 0, z = 1 + (1 + z018 + z114) + z1, z018 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U11(mark(z017), z113), z1) + MARK(1 + z017 + z113) :|: z1 >= 0, z = 1 + (1 + z017 + z113) + z1, z113 >= 0, z017 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(3, z1) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 MARK(z) -{ 1 }-> 1 + A__U12(2, z1) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 MARK(z) -{ 1 }-> 1 + A__U12(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 MARK(z) -{ 1 }-> 1 + A__U12(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U12(0, z1) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 MARK(z) -{ 1 }-> 1 + A__U12(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 MARK(z) -{ 1 }-> 1 + A__U12(1 + mark(z025), z1) + MARK(1 + z025) :|: z025 >= 0, z1 >= 0, z = 1 + (1 + z025) + z1 MARK(z) -{ 1 }-> 1 + A__U12(1 + mark(z024) + z119, z1) + MARK(1 + z024 + z119) :|: z1 >= 0, z024 >= 0, z = 1 + (1 + z024 + z119) + z1, z119 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(1 + 0 + 3, z1) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 MARK(z) -{ 1 }-> 1 + A__U11(a__take(mark(z014), mark(z111)), z1) + MARK(1 + z014 + z111) :|: z = 1 + (1 + z014 + z111) + z1, z1 >= 0, z014 >= 0, z111 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__length(mark(z010)), z1) + MARK(1 + z010) :|: z1 >= 0, z = 1 + (1 + z010) + z1, z010 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U23(mark(z013), z110, z24, z34), z1) + MARK(1 + z013 + z110 + z24 + z34) :|: z110 >= 0, z1 >= 0, z = 1 + (1 + z013 + z110 + z24 + z34) + z1, z013 >= 0, z24 >= 0, z34 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U22(mark(z012), z19, z23, z33), z1) + MARK(1 + z012 + z19 + z23 + z33) :|: z1 >= 0, z19 >= 0, z23 >= 0, z012 >= 0, z = 1 + (1 + z012 + z19 + z23 + z33) + z1, z33 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U21(mark(z011), z18, z22, z32), z1) + MARK(1 + z011 + z18 + z22 + z32) :|: z18 >= 0, z011 >= 0, z32 >= 0, z1 >= 0, z = 1 + (1 + z011 + z18 + z22 + z32) + z1, z22 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U12(mark(z09), z17), z1) + MARK(1 + z09 + z17) :|: z1 >= 0, z17 >= 0, z = 1 + (1 + z09 + z17) + z1, z09 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U11(mark(z08), z16), z1) + MARK(1 + z08 + z16) :|: z08 >= 0, z1 >= 0, z16 >= 0, z = 1 + (1 + z08 + z16) + z1 MARK(z) -{ 1 }-> 1 + A__U11(3, z1) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 MARK(z) -{ 1 }-> 1 + A__U11(2, z1) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 MARK(z) -{ 1 }-> 1 + A__U11(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 MARK(z) -{ 1 }-> 1 + A__U11(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U11(0, z1) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 MARK(z) -{ 1 }-> 1 + A__U11(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z016), z1) + MARK(1 + z016) :|: z1 >= 0, z016 >= 0, z = 1 + (1 + z016) + z1 MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z015) + z112, z1) + MARK(1 + z015 + z112) :|: z015 >= 0, z1 >= 0, z112 >= 0, z = 1 + (1 + z015 + z112) + z1 MARK(z) -{ 1 }-> 1 + A__U11(1 + 0 + 3, z1) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 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(z032), mark(z125))) + MARK(1 + z032 + z125) :|: z032 >= 0, z = 1 + (1 + z032 + z125), z125 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__length(mark(z028))) + MARK(1 + z028) :|: z028 >= 0, z = 1 + (1 + z028) MARK(z) -{ 1 }-> 1 + A__LENGTH(a__U23(mark(z031), z124, z210, z310)) + MARK(1 + z031 + z124 + z210 + z310) :|: z031 >= 0, z124 >= 0, z310 >= 0, z210 >= 0, z = 1 + (1 + z031 + z124 + z210 + z310) MARK(z) -{ 1 }-> 1 + A__LENGTH(a__U22(mark(z030), z123, z29, z39)) + MARK(1 + z030 + z123 + z29 + z39) :|: z = 1 + (1 + z030 + z123 + z29 + z39), z29 >= 0, z39 >= 0, z123 >= 0, z030 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__U21(mark(z029), z122, z28, z38)) + MARK(1 + z029 + z122 + z28 + z38) :|: z029 >= 0, z = 1 + (1 + z029 + z122 + z28 + z38), z28 >= 0, z38 >= 0, z122 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__U12(mark(z027), z121)) + MARK(1 + z027 + z121) :|: z = 1 + (1 + z027 + z121), z121 >= 0, z027 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__U11(mark(z026), z120)) + MARK(1 + z026 + z120) :|: z120 >= 0, z = 1 + (1 + z026 + z120), z026 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(3) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__LENGTH(2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__LENGTH(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z034)) + MARK(1 + z034) :|: z034 >= 0, z = 1 + (1 + z034) MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z033) + z126) + MARK(1 + z033 + z126) :|: z = 1 + (1 + z033 + z126), z033 >= 0, z126 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + 0 + 3) + MARK(3) :|: z = 1 + 3 a__U11(z, z') -{ 0 }-> a__U12(2, z0) :|: z = 2, z0 >= 0, z' = z0 a__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U11(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U12(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U12(z, z') -{ 0 }-> 1 + a__length(a__take(mark(z0338), mark(z1263))) :|: z = 2, z0338 >= 0, z1263 >= 0, z' = 1 + z0338 + z1263 a__U12(z, z') -{ 0 }-> 1 + a__length(a__length(mark(z0334))) :|: z = 2, z0334 >= 0, z' = 1 + z0334 a__U12(z, z') -{ 0 }-> 1 + a__length(a__U23(mark(z0337), z1262, z2112, z3112)) :|: z = 2, z3112 >= 0, z0337 >= 0, z1262 >= 0, z' = 1 + z0337 + z1262 + z2112 + z3112, z2112 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(a__U22(mark(z0336), z1261, z2111, z3111)) :|: z = 2, z2111 >= 0, z' = 1 + z0336 + z1261 + z2111 + z3111, z1261 >= 0, z3111 >= 0, z0336 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(a__U21(mark(z0335), z1260, z2110, z3110)) :|: z = 2, z' = 1 + z0335 + z1260 + z2110 + z3110, z2110 >= 0, z0335 >= 0, z3110 >= 0, z1260 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(a__U12(mark(z0333), z1259)) :|: z = 2, z' = 1 + z0333 + z1259, z1259 >= 0, z0333 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(a__U11(mark(z0332), z1258)) :|: z = 2, z1258 >= 0, z' = 1 + z0332 + z1258, z0332 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(3) :|: z = 2, z' = 3 a__U12(z, z') -{ 0 }-> 1 + a__length(2) :|: z = 2, z' = 2 a__U12(z, z') -{ 0 }-> 1 + a__length(1) :|: z = 2, z' = 1 a__U12(z, z') -{ 0 }-> 1 + a__length(0) :|: z = 2, z' = 0 a__U12(z, z') -{ 0 }-> 1 + a__length(0) :|: z = 2, z0 >= 0, z' = z0 a__U12(z, z') -{ 0 }-> 1 + a__length(0) :|: z = 2, z' = 3 a__U12(z, z') -{ 0 }-> 1 + a__length(1 + mark(z0340)) :|: z = 2, z' = 1 + z0340, z0340 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(1 + mark(z0339) + z1264) :|: z = 2, z' = 1 + z0339 + z1264, z1264 >= 0, z0339 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(1 + 0 + 3) :|: z = 2, z' = 3 a__U12(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U21(z, z', z'', z4) -{ 0 }-> a__U22(2, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U21(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U21(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__U22(z, z', z'', z4) -{ 0 }-> a__U23(2, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U22(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U22(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__U23(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U23(z, z', z'', z4) -{ 0 }-> 1 + mark(z2) + (1 + z1 + z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U23(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__length(z) -{ 0 }-> a__U11(2, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 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__take(z, z') -{ 0 }-> a__U21(2, z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 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__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(z0365), mark(z1284))) :|: z = 1 + (1 + z0365 + z1284), z0365 >= 0, z1284 >= 0 mark(z) -{ 0 }-> a__length(a__length(mark(z0361))) :|: z0361 >= 0, z = 1 + (1 + z0361) mark(z) -{ 0 }-> a__length(a__U23(mark(z0364), z1283, z2121, z3121)) :|: z2121 >= 0, z1283 >= 0, z = 1 + (1 + z0364 + z1283 + z2121 + z3121), z3121 >= 0, z0364 >= 0 mark(z) -{ 0 }-> a__length(a__U22(mark(z0363), z1282, z2120, z3120)) :|: z = 1 + (1 + z0363 + z1282 + z2120 + z3120), z1282 >= 0, z3120 >= 0, z2120 >= 0, z0363 >= 0 mark(z) -{ 0 }-> a__length(a__U21(mark(z0362), z1281, z2119, z3119)) :|: z2119 >= 0, z1281 >= 0, z3119 >= 0, z = 1 + (1 + z0362 + z1281 + z2119 + z3119), z0362 >= 0 mark(z) -{ 0 }-> a__length(a__U12(mark(z0360), z1280)) :|: z = 1 + (1 + z0360 + z1280), z0360 >= 0, z1280 >= 0 mark(z) -{ 0 }-> a__length(a__U11(mark(z0359), z1279)) :|: z = 1 + (1 + z0359 + z1279), z0359 >= 0, z1279 >= 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(z0367)) :|: z = 1 + (1 + z0367), z0367 >= 0 mark(z) -{ 0 }-> a__length(1 + mark(z0366) + z1285) :|: z1285 >= 0, z0366 >= 0, z = 1 + (1 + z0366 + z1285) mark(z) -{ 0 }-> a__length(1 + 0 + 3) :|: z = 1 + 3 mark(z) -{ 0 }-> a__U23(a__take(mark(z0392), mark(z1305)), z1, z2, z3) :|: z1305 >= 0, z1 >= 0, z0392 >= 0, z = 1 + (1 + z0392 + z1305) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__length(mark(z0388)), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0388) + z1 + z2 + z3, z0388 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__U23(mark(z0391), z1304, z2130, z3130), z1, z2, z3) :|: z3130 >= 0, z1304 >= 0, z1 >= 0, z = 1 + (1 + z0391 + z1304 + z2130 + z3130) + z1 + z2 + z3, z2130 >= 0, z0391 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__U22(mark(z0390), z1303, z2129, z3129), z1, z2, z3) :|: z2129 >= 0, z1 >= 0, z = 1 + (1 + z0390 + z1303 + z2129 + z3129) + z1 + z2 + z3, z0390 >= 0, z1303 >= 0, z3129 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__U21(mark(z0389), z1302, z2128, z3128), z1, z2, z3) :|: z3128 >= 0, z1 >= 0, z1302 >= 0, z2128 >= 0, z = 1 + (1 + z0389 + z1302 + z2128 + z3128) + z1 + z2 + z3, z0389 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__U12(mark(z0387), z1301), z1, z2, z3) :|: z1301 >= 0, z1 >= 0, z0387 >= 0, z = 1 + (1 + z0387 + z1301) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__U11(mark(z0386), z1300), z1, z2, z3) :|: z = 1 + (1 + z0386 + z1300) + z1 + z2 + z3, z0386 >= 0, z1300 >= 0, z1 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(3, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(2, z1, z2, z3) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(1, z1, z2, z3) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(0, z1, z2, z3) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(0, z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(0, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(1 + mark(z0394), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0394) + z1 + z2 + z3, z0394 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(1 + mark(z0393) + z1306, z1, z2, z3) :|: z = 1 + (1 + z0393 + z1306) + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0, z0393 >= 0, z1306 >= 0 mark(z) -{ 0 }-> a__U23(1 + 0 + 3, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(a__take(mark(z0383), mark(z1298)), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0383 + z1298) + z1 + z2 + z3, z1298 >= 0, z2 >= 0, z3 >= 0, z0383 >= 0 mark(z) -{ 0 }-> a__U22(a__length(mark(z0379)), z1, z2, z3) :|: z = 1 + (1 + z0379) + z1 + z2 + z3, z1 >= 0, z0379 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(a__U23(mark(z0382), z1297, z2127, z3127), z1, z2, z3) :|: z0382 >= 0, z1 >= 0, z2127 >= 0, z = 1 + (1 + z0382 + z1297 + z2127 + z3127) + z1 + z2 + z3, z3127 >= 0, z2 >= 0, z3 >= 0, z1297 >= 0 mark(z) -{ 0 }-> a__U22(a__U22(mark(z0381), z1296, z2126, z3126), z1, z2, z3) :|: z1296 >= 0, z2126 >= 0, z1 >= 0, z = 1 + (1 + z0381 + z1296 + z2126 + z3126) + z1 + z2 + z3, z0381 >= 0, z3126 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(a__U21(mark(z0380), z1295, z2125, z3125), z1, z2, z3) :|: z2125 >= 0, z1 >= 0, z1295 >= 0, z0380 >= 0, z3125 >= 0, z = 1 + (1 + z0380 + z1295 + z2125 + z3125) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(a__U12(mark(z0378), z1294), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0378 + z1294) + z1 + z2 + z3, z0378 >= 0, z1294 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(a__U11(mark(z0377), z1293), z1, z2, z3) :|: z1 >= 0, z0377 >= 0, z1293 >= 0, z = 1 + (1 + z0377 + z1293) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(3, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(2, z1, z2, z3) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(1, z1, z2, z3) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(0, z1, z2, z3) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(0, z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(0, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(1 + mark(z0385), z1, z2, z3) :|: z1 >= 0, z0385 >= 0, z = 1 + (1 + z0385) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(1 + mark(z0384) + z1299, z1, z2, z3) :|: z1 >= 0, z1299 >= 0, z0384 >= 0, z = 1 + (1 + z0384 + z1299) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(1 + 0 + 3, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(a__take(mark(z0374), mark(z1291)), z1, z2, z3) :|: z1 >= 0, z1291 >= 0, z = 1 + (1 + z0374 + z1291) + z1 + z2 + z3, z0374 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(a__length(mark(z0370)), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0370) + z1 + z2 + z3, z0370 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(a__U23(mark(z0373), z1290, z2124, z3124), z1, z2, z3) :|: z = 1 + (1 + z0373 + z1290 + z2124 + z3124) + z1 + z2 + z3, z3124 >= 0, z1 >= 0, z1290 >= 0, z2124 >= 0, z2 >= 0, z3 >= 0, z0373 >= 0 mark(z) -{ 0 }-> a__U21(a__U22(mark(z0372), z1289, z2123, z3123), z1, z2, z3) :|: z0372 >= 0, z1 >= 0, z1289 >= 0, z3123 >= 0, z = 1 + (1 + z0372 + z1289 + z2123 + z3123) + z1 + z2 + z3, z2123 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(a__U21(mark(z0371), z1288, z2122, z3122), z1, z2, z3) :|: z2122 >= 0, z1 >= 0, z0371 >= 0, z3122 >= 0, z = 1 + (1 + z0371 + z1288 + z2122 + z3122) + z1 + z2 + z3, z1288 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(a__U12(mark(z0369), z1287), z1, z2, z3) :|: z1 >= 0, z0369 >= 0, z = 1 + (1 + z0369 + z1287) + z1 + z2 + z3, z2 >= 0, z3 >= 0, z1287 >= 0 mark(z) -{ 0 }-> a__U21(a__U11(mark(z0368), z1286), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0368 + z1286) + z1 + z2 + z3, z0368 >= 0, z1286 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(3, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(2, z1, z2, z3) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(1, z1, z2, z3) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(0, z1, z2, z3) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(0, z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(0, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(1 + mark(z0376), z1, z2, z3) :|: z0376 >= 0, z1 >= 0, z = 1 + (1 + z0376) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(1 + mark(z0375) + z1292, z1, z2, z3) :|: z1292 >= 0, z = 1 + (1 + z0375 + z1292) + z1 + z2 + z3, z1 >= 0, z0375 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(1 + 0 + 3, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U12(a__take(mark(z0356), mark(z1277)), z1) :|: z1 >= 0, z = 1 + (1 + z0356 + z1277) + z1, z0356 >= 0, z1277 >= 0 mark(z) -{ 0 }-> a__U12(a__length(mark(z0352)), z1) :|: z1 >= 0, z = 1 + (1 + z0352) + z1, z0352 >= 0 mark(z) -{ 0 }-> a__U12(a__U23(mark(z0355), z1276, z2118, z3118), z1) :|: z = 1 + (1 + z0355 + z1276 + z2118 + z3118) + z1, z1 >= 0, z0355 >= 0, z2118 >= 0, z3118 >= 0, z1276 >= 0 mark(z) -{ 0 }-> a__U12(a__U22(mark(z0354), z1275, z2117, z3117), z1) :|: z3117 >= 0, z1 >= 0, z1275 >= 0, z = 1 + (1 + z0354 + z1275 + z2117 + z3117) + z1, z2117 >= 0, z0354 >= 0 mark(z) -{ 0 }-> a__U12(a__U21(mark(z0353), z1274, z2116, z3116), z1) :|: z1 >= 0, z2116 >= 0, z1274 >= 0, z = 1 + (1 + z0353 + z1274 + z2116 + z3116) + z1, z3116 >= 0, z0353 >= 0 mark(z) -{ 0 }-> a__U12(a__U12(mark(z0351), z1273), z1) :|: z1 >= 0, z = 1 + (1 + z0351 + z1273) + z1, z0351 >= 0, z1273 >= 0 mark(z) -{ 0 }-> a__U12(a__U11(mark(z0350), z1272), z1) :|: z1 >= 0, z0350 >= 0, z1272 >= 0, z = 1 + (1 + z0350 + z1272) + z1 mark(z) -{ 0 }-> a__U12(3, z1) :|: z1 >= 0, z = 1 + 3 + z1 mark(z) -{ 0 }-> a__U12(2, z1) :|: z1 >= 0, z = 1 + 2 + z1 mark(z) -{ 0 }-> a__U12(1, z1) :|: z1 >= 0, z = 1 + 1 + z1 mark(z) -{ 0 }-> a__U12(0, z1) :|: z1 >= 0, z = 1 + 0 + z1 mark(z) -{ 0 }-> a__U12(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U12(0, z1) :|: z1 >= 0, z = 1 + 3 + z1 mark(z) -{ 0 }-> a__U12(1 + mark(z0358), z1) :|: z1 >= 0, z = 1 + (1 + z0358) + z1, z0358 >= 0 mark(z) -{ 0 }-> a__U12(1 + mark(z0357) + z1278, z1) :|: z = 1 + (1 + z0357 + z1278) + z1, z1 >= 0, z0357 >= 0, z1278 >= 0 mark(z) -{ 0 }-> a__U12(1 + 0 + 3, z1) :|: z1 >= 0, z = 1 + 3 + z1 mark(z) -{ 0 }-> a__U11(a__take(mark(z0347), mark(z1270)), z1) :|: z1 >= 0, z0347 >= 0, z1270 >= 0, z = 1 + (1 + z0347 + z1270) + z1 mark(z) -{ 0 }-> a__U11(a__length(mark(z0343)), z1) :|: z1 >= 0, z = 1 + (1 + z0343) + z1, z0343 >= 0 mark(z) -{ 0 }-> a__U11(a__U23(mark(z0346), z1269, z2115, z3115), z1) :|: z2115 >= 0, z1 >= 0, z1269 >= 0, z3115 >= 0, z0346 >= 0, z = 1 + (1 + z0346 + z1269 + z2115 + z3115) + z1 mark(z) -{ 0 }-> a__U11(a__U22(mark(z0345), z1268, z2114, z3114), z1) :|: z1268 >= 0, z1 >= 0, z0345 >= 0, z = 1 + (1 + z0345 + z1268 + z2114 + z3114) + z1, z3114 >= 0, z2114 >= 0 mark(z) -{ 0 }-> a__U11(a__U21(mark(z0344), z1267, z2113, z3113), z1) :|: z3113 >= 0, z0344 >= 0, z1 >= 0, z2113 >= 0, z = 1 + (1 + z0344 + z1267 + z2113 + z3113) + z1, z1267 >= 0 mark(z) -{ 0 }-> a__U11(a__U12(mark(z0342), z1266), z1) :|: z1 >= 0, z = 1 + (1 + z0342 + z1266) + z1, z0342 >= 0, z1266 >= 0 mark(z) -{ 0 }-> a__U11(a__U11(mark(z0341), z1265), z1) :|: z = 1 + (1 + z0341 + z1265) + z1, z0341 >= 0, z1 >= 0, z1265 >= 0 mark(z) -{ 0 }-> a__U11(3, z1) :|: z1 >= 0, z = 1 + 3 + z1 mark(z) -{ 0 }-> a__U11(2, z1) :|: z1 >= 0, z = 1 + 2 + z1 mark(z) -{ 0 }-> a__U11(1, z1) :|: z1 >= 0, z = 1 + 1 + z1 mark(z) -{ 0 }-> a__U11(0, z1) :|: z1 >= 0, z = 1 + 0 + z1 mark(z) -{ 0 }-> a__U11(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U11(0, z1) :|: z1 >= 0, z = 1 + 3 + z1 mark(z) -{ 0 }-> a__U11(1 + mark(z0349), z1) :|: z1 >= 0, z0349 >= 0, z = 1 + (1 + z0349) + z1 mark(z) -{ 0 }-> a__U11(1 + mark(z0348) + z1271, z1) :|: z1271 >= 0, z0348 >= 0, z1 >= 0, z = 1 + (1 + z0348 + z1271) + z1 mark(z) -{ 0 }-> a__U11(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__LENGTH(z) -{ 1 }-> 1 + A__U11(2, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAKE(z, z') -{ 1 }-> 1 + A__U21(2, z2, z - 1, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 A__U11(z, z') -{ 1 }-> 1 + A__U12(2, z') :|: z = 2, z' >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__take(mark(z05), mark(z14))) + MARK(1 + z05 + z14) :|: z = 2, z' = 1 + z05 + z14, z05 >= 0, z14 >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__length(mark(z' - 1))) + MARK(1 + (z' - 1)) :|: z = 2, z' - 1 >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__U23(mark(z04), z13, z21, z31)) + MARK(1 + z04 + z13 + z21 + z31) :|: z = 2, z04 >= 0, z21 >= 0, z31 >= 0, z' = 1 + z04 + z13 + z21 + z31, z13 >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__U22(mark(z03), z12, z2'', z3'')) + MARK(1 + z03 + z12 + z2'' + z3'') :|: z = 2, z' = 1 + z03 + z12 + z2'' + z3'', z12 >= 0, z3'' >= 0, z03 >= 0, z2'' >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__U21(mark(z02), z11, z2', z3')) + MARK(1 + z02 + z11 + z2' + z3') :|: z = 2, z' = 1 + z02 + z11 + z2' + z3', z11 >= 0, z3' >= 0, z02 >= 0, z2' >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__U12(mark(z0''), z1'')) + MARK(1 + z0'' + z1'') :|: z = 2, z0'' >= 0, z' = 1 + z0'' + z1'', z1'' >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(a__U11(mark(z0'), z1')) + MARK(1 + z0' + z1') :|: z = 2, z0' >= 0, z1' >= 0, z' = 1 + z0' + z1' A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(3) + MARK(3) :|: z = 2, z' = 3 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(2) + MARK(2) :|: z = 2, z' = 2 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(1) + MARK(1) :|: z = 2, z' = 1 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(0) + MARK(z') :|: z = 2, z' >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(0) + MARK(3) :|: z = 2, z' = 3 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(0) + MARK(0) :|: z = 2, z' = 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(1 + mark(z' - 1)) + MARK(1 + (z' - 1)) :|: z = 2, z' - 1 >= 0 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(1 + mark(z06) + z15) + MARK(1 + z06 + z15) :|: z = 2, z15 >= 0, z06 >= 0, z' = 1 + z06 + z15 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(1 + 0 + 3) + MARK(3) :|: z = 2, z' = 3 A__U21(z, z', z'', z4) -{ 1 }-> 1 + A__U22(2, z', z'', z4) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0 A__U22(z, z', z'', z4) -{ 1 }-> 1 + A__U23(2, z', z'', z4) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0 A__U23(z, z', z'', z4) -{ 1 }-> 1 + MARK(z4) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 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__U23(a__take(mark(z059), mark(z146)), z1, z2, z3) + MARK(1 + z059 + z146) :|: z1 >= 0, z = 1 + (1 + z059 + z146) + z1 + z2 + z3, z059 >= 0, z2 >= 0, z3 >= 0, z146 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__length(mark(z055)), z1, z2, z3) + MARK(1 + z055) :|: z1 >= 0, z055 >= 0, z = 1 + (1 + z055) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__U23(mark(z058), z145, z219, z319), z1, z2, z3) + MARK(1 + z058 + z145 + z219 + z319) :|: z319 >= 0, z145 >= 0, z = 1 + (1 + z058 + z145 + z219 + z319) + z1 + z2 + z3, z1 >= 0, z219 >= 0, z058 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__U22(mark(z057), z144, z218, z318), z1, z2, z3) + MARK(1 + z057 + z144 + z218 + z318) :|: z = 1 + (1 + z057 + z144 + z218 + z318) + z1 + z2 + z3, z1 >= 0, z144 >= 0, z318 >= 0, z218 >= 0, z2 >= 0, z3 >= 0, z057 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__U21(mark(z056), z143, z217, z317), z1, z2, z3) + MARK(1 + z056 + z143 + z217 + z317) :|: z056 >= 0, z1 >= 0, z217 >= 0, z143 >= 0, z317 >= 0, z = 1 + (1 + z056 + z143 + z217 + z317) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__U12(mark(z054), z142), z1, z2, z3) + MARK(1 + z054 + z142) :|: z1 >= 0, z = 1 + (1 + z054 + z142) + z1 + z2 + z3, z054 >= 0, z142 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(a__U11(mark(z053), z141), z1, z2, z3) + MARK(1 + z053 + z141) :|: z141 >= 0, z1 >= 0, z053 >= 0, z = 1 + (1 + z053 + z141) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(3, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(2, z1, z2, z3) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(1, z1, z2, z3) + MARK(1) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(0, z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(0, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(0, z1, z2, z3) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(1 + mark(z061), z1, z2, z3) + MARK(1 + z061) :|: z = 1 + (1 + z061) + z1 + z2 + z3, z1 >= 0, z061 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(1 + mark(z060) + z147, z1, z2, z3) + MARK(1 + z060 + z147) :|: z1 >= 0, z = 1 + (1 + z060 + z147) + z1 + z2 + z3, z147 >= 0, z060 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U23(1 + 0 + 3, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__take(mark(z050), mark(z139)), z1, z2, z3) + MARK(1 + z050 + z139) :|: z1 >= 0, z139 >= 0, z = 1 + (1 + z050 + z139) + z1 + z2 + z3, z050 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__length(mark(z046)), z1, z2, z3) + MARK(1 + z046) :|: z046 >= 0, z1 >= 0, z2 >= 0, z3 >= 0, z = 1 + (1 + z046) + z1 + z2 + z3 MARK(z) -{ 1 }-> 1 + A__U22(a__U23(mark(z049), z138, z216, z316), z1, z2, z3) + MARK(1 + z049 + z138 + z216 + z316) :|: z216 >= 0, z1 >= 0, z049 >= 0, z138 >= 0, z316 >= 0, z = 1 + (1 + z049 + z138 + z216 + z316) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__U22(mark(z048), z137, z215, z315), z1, z2, z3) + MARK(1 + z048 + z137 + z215 + z315) :|: z315 >= 0, z = 1 + (1 + z048 + z137 + z215 + z315) + z1 + z2 + z3, z1 >= 0, z048 >= 0, z137 >= 0, z2 >= 0, z3 >= 0, z215 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__U21(mark(z047), z136, z214, z314), z1, z2, z3) + MARK(1 + z047 + z136 + z214 + z314) :|: z = 1 + (1 + z047 + z136 + z214 + z314) + z1 + z2 + z3, z1 >= 0, z214 >= 0, z2 >= 0, z3 >= 0, z047 >= 0, z136 >= 0, z314 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__U12(mark(z045), z135), z1, z2, z3) + MARK(1 + z045 + z135) :|: z1 >= 0, z045 >= 0, z = 1 + (1 + z045 + z135) + z1 + z2 + z3, z135 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(a__U11(mark(z044), z134), z1, z2, z3) + MARK(1 + z044 + z134) :|: z1 >= 0, z134 >= 0, z044 >= 0, z = 1 + (1 + z044 + z134) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(3, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(2, z1, z2, z3) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(1, z1, z2, z3) + MARK(1) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(0, z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(0, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(0, z1, z2, z3) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(1 + mark(z052), z1, z2, z3) + MARK(1 + z052) :|: z052 >= 0, z1 >= 0, z = 1 + (1 + z052) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(1 + mark(z051) + z140, z1, z2, z3) + MARK(1 + z051 + z140) :|: z1 >= 0, z = 1 + (1 + z051 + z140) + z1 + z2 + z3, z051 >= 0, z140 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(1 + 0 + 3, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__take(mark(z041), mark(z132)), z1, z2, z3) + MARK(1 + z041 + z132) :|: z1 >= 0, z = 1 + (1 + z041 + z132) + z1 + z2 + z3, z132 >= 0, z041 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__length(mark(z037)), z1, z2, z3) + MARK(1 + z037) :|: z = 1 + (1 + z037) + z1 + z2 + z3, z1 >= 0, z037 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U23(mark(z040), z131, z213, z313), z1, z2, z3) + MARK(1 + z040 + z131 + z213 + z313) :|: z131 >= 0, z1 >= 0, z213 >= 0, z040 >= 0, z313 >= 0, z = 1 + (1 + z040 + z131 + z213 + z313) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U22(mark(z039), z130, z212, z312), z1, z2, z3) + MARK(1 + z039 + z130 + z212 + z312) :|: z212 >= 0, z130 >= 0, z1 >= 0, z039 >= 0, z312 >= 0, z = 1 + (1 + z039 + z130 + z212 + z312) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U21(mark(z038), z129, z211, z311), z1, z2, z3) + MARK(1 + z038 + z129 + z211 + z311) :|: z311 >= 0, z = 1 + (1 + z038 + z129 + z211 + z311) + z1 + z2 + z3, z1 >= 0, z129 >= 0, z211 >= 0, z038 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U12(mark(z036), z128), z1, z2, z3) + MARK(1 + z036 + z128) :|: z = 1 + (1 + z036 + z128) + z1 + z2 + z3, z036 >= 0, z1 >= 0, z128 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U11(mark(z035), z127), z1, z2, z3) + MARK(1 + z035 + z127) :|: z035 >= 0, z1 >= 0, z = 1 + (1 + z035 + z127) + z1 + z2 + z3, z127 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(3, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(2, z1, z2, z3) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1, z1, z2, z3) + MARK(1) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(0, z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(0, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(0, z1, z2, z3) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1 + mark(z043), z1, z2, z3) + MARK(1 + z043) :|: z1 >= 0, z043 >= 0, z = 1 + (1 + z043) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1 + mark(z042) + z133, z1, z2, z3) + MARK(1 + z042 + z133) :|: z042 >= 0, z1 >= 0, z133 >= 0, z = 1 + (1 + z042 + z133) + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1 + 0 + 3, z1, z2, z3) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__take(mark(z023), mark(z118)), z1) + MARK(1 + z023 + z118) :|: z1 >= 0, z118 >= 0, z = 1 + (1 + z023 + z118) + z1, z023 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__length(mark(z019)), z1) + MARK(1 + z019) :|: z019 >= 0, z1 >= 0, z = 1 + (1 + z019) + z1 MARK(z) -{ 1 }-> 1 + A__U12(a__U23(mark(z022), z117, z27, z37), z1) + MARK(1 + z022 + z117 + z27 + z37) :|: z117 >= 0, z1 >= 0, z022 >= 0, z = 1 + (1 + z022 + z117 + z27 + z37) + z1, z27 >= 0, z37 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U22(mark(z021), z116, z26, z36), z1) + MARK(1 + z021 + z116 + z26 + z36) :|: z021 >= 0, z = 1 + (1 + z021 + z116 + z26 + z36) + z1, z1 >= 0, z26 >= 0, z36 >= 0, z116 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U21(mark(z020), z115, z25, z35), z1) + MARK(1 + z020 + z115 + z25 + z35) :|: z25 >= 0, z1 >= 0, z = 1 + (1 + z020 + z115 + z25 + z35) + z1, z35 >= 0, z115 >= 0, z020 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U12(mark(z018), z114), z1) + MARK(1 + z018 + z114) :|: z114 >= 0, z1 >= 0, z = 1 + (1 + z018 + z114) + z1, z018 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U11(mark(z017), z113), z1) + MARK(1 + z017 + z113) :|: z1 >= 0, z = 1 + (1 + z017 + z113) + z1, z113 >= 0, z017 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(3, z - 4) + MARK(3) :|: z - 4 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(2, z - 3) + MARK(2) :|: z - 3 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(1, z - 2) + MARK(1) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U12(0, z - 4) + MARK(3) :|: z - 4 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(0, z - 1) + MARK(0) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(1 + mark(z025), z1) + MARK(1 + z025) :|: z025 >= 0, z1 >= 0, z = 1 + (1 + z025) + z1 MARK(z) -{ 1 }-> 1 + A__U12(1 + mark(z024) + z119, z1) + MARK(1 + z024 + z119) :|: z1 >= 0, z024 >= 0, z = 1 + (1 + z024 + z119) + z1, z119 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(1 + 0 + 3, z - 4) + MARK(3) :|: z - 4 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__take(mark(z014), mark(z111)), z1) + MARK(1 + z014 + z111) :|: z = 1 + (1 + z014 + z111) + z1, z1 >= 0, z014 >= 0, z111 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__length(mark(z010)), z1) + MARK(1 + z010) :|: z1 >= 0, z = 1 + (1 + z010) + z1, z010 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U23(mark(z013), z110, z24, z34), z1) + MARK(1 + z013 + z110 + z24 + z34) :|: z110 >= 0, z1 >= 0, z = 1 + (1 + z013 + z110 + z24 + z34) + z1, z013 >= 0, z24 >= 0, z34 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U22(mark(z012), z19, z23, z33), z1) + MARK(1 + z012 + z19 + z23 + z33) :|: z1 >= 0, z19 >= 0, z23 >= 0, z012 >= 0, z = 1 + (1 + z012 + z19 + z23 + z33) + z1, z33 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U21(mark(z011), z18, z22, z32), z1) + MARK(1 + z011 + z18 + z22 + z32) :|: z18 >= 0, z011 >= 0, z32 >= 0, z1 >= 0, z = 1 + (1 + z011 + z18 + z22 + z32) + z1, z22 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U12(mark(z09), z17), z1) + MARK(1 + z09 + z17) :|: z1 >= 0, z17 >= 0, z = 1 + (1 + z09 + z17) + z1, z09 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U11(mark(z08), z16), z1) + MARK(1 + z08 + z16) :|: z08 >= 0, z1 >= 0, z16 >= 0, z = 1 + (1 + z08 + z16) + z1 MARK(z) -{ 1 }-> 1 + A__U11(3, z - 4) + MARK(3) :|: z - 4 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(2, z - 3) + MARK(2) :|: z - 3 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(1, z - 2) + MARK(1) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U11(0, z - 4) + MARK(3) :|: z - 4 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(0, z - 1) + MARK(0) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z016), z1) + MARK(1 + z016) :|: z1 >= 0, z016 >= 0, z = 1 + (1 + z016) + z1 MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z015) + z112, z1) + MARK(1 + z015 + z112) :|: z015 >= 0, z1 >= 0, z112 >= 0, z = 1 + (1 + z015 + z112) + z1 MARK(z) -{ 1 }-> 1 + A__U11(1 + 0 + 3, z - 4) + MARK(3) :|: z - 4 >= 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(z032), mark(z125))) + MARK(1 + z032 + z125) :|: z032 >= 0, z = 1 + (1 + z032 + z125), z125 >= 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__U23(mark(z031), z124, z210, z310)) + MARK(1 + z031 + z124 + z210 + z310) :|: z031 >= 0, z124 >= 0, z310 >= 0, z210 >= 0, z = 1 + (1 + z031 + z124 + z210 + z310) MARK(z) -{ 1 }-> 1 + A__LENGTH(a__U22(mark(z030), z123, z29, z39)) + MARK(1 + z030 + z123 + z29 + z39) :|: z = 1 + (1 + z030 + z123 + z29 + z39), z29 >= 0, z39 >= 0, z123 >= 0, z030 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__U21(mark(z029), z122, z28, z38)) + MARK(1 + z029 + z122 + z28 + z38) :|: z029 >= 0, z = 1 + (1 + z029 + z122 + z28 + z38), z28 >= 0, z38 >= 0, z122 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__U12(mark(z027), z121)) + MARK(1 + z027 + z121) :|: z = 1 + (1 + z027 + z121), z121 >= 0, z027 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__U11(mark(z026), z120)) + MARK(1 + z026 + z120) :|: z120 >= 0, z = 1 + (1 + z026 + z120), z026 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(3) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__LENGTH(2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__LENGTH(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z033) + z126) + MARK(1 + z033 + z126) :|: z = 1 + (1 + z033 + z126), z033 >= 0, z126 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + 0 + 3) + MARK(3) :|: z = 1 + 3 a__U11(z, z') -{ 0 }-> a__U12(2, z') :|: z = 2, z' >= 0 a__U11(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U11(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U12(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(a__take(mark(z0338), mark(z1263))) :|: z = 2, z0338 >= 0, z1263 >= 0, z' = 1 + z0338 + z1263 a__U12(z, z') -{ 0 }-> 1 + a__length(a__length(mark(z' - 1))) :|: z = 2, z' - 1 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(a__U23(mark(z0337), z1262, z2112, z3112)) :|: z = 2, z3112 >= 0, z0337 >= 0, z1262 >= 0, z' = 1 + z0337 + z1262 + z2112 + z3112, z2112 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(a__U22(mark(z0336), z1261, z2111, z3111)) :|: z = 2, z2111 >= 0, z' = 1 + z0336 + z1261 + z2111 + z3111, z1261 >= 0, z3111 >= 0, z0336 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(a__U21(mark(z0335), z1260, z2110, z3110)) :|: z = 2, z' = 1 + z0335 + z1260 + z2110 + z3110, z2110 >= 0, z0335 >= 0, z3110 >= 0, z1260 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(a__U12(mark(z0333), z1259)) :|: z = 2, z' = 1 + z0333 + z1259, z1259 >= 0, z0333 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(a__U11(mark(z0332), z1258)) :|: z = 2, z1258 >= 0, z' = 1 + z0332 + z1258, z0332 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(3) :|: z = 2, z' = 3 a__U12(z, z') -{ 0 }-> 1 + a__length(2) :|: z = 2, z' = 2 a__U12(z, z') -{ 0 }-> 1 + a__length(1) :|: z = 2, z' = 1 a__U12(z, z') -{ 0 }-> 1 + a__length(0) :|: z = 2, z' = 0 a__U12(z, z') -{ 0 }-> 1 + a__length(0) :|: z = 2, z' >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(0) :|: z = 2, z' = 3 a__U12(z, z') -{ 0 }-> 1 + a__length(1 + mark(z' - 1)) :|: z = 2, z' - 1 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(1 + mark(z0339) + z1264) :|: z = 2, z' = 1 + z0339 + z1264, z1264 >= 0, z0339 >= 0 a__U12(z, z') -{ 0 }-> 1 + a__length(1 + 0 + 3) :|: z = 2, z' = 3 a__U12(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U21(z, z', z'', z4) -{ 0 }-> a__U22(2, z', z'', z4) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0 a__U21(z, z', z'', z4) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z4 >= 0 a__U21(z, z', z'', z4) -{ 0 }-> 1 + z + z' + z'' + z4 :|: z' >= 0, z >= 0, z'' >= 0, z4 >= 0 a__U22(z, z', z'', z4) -{ 0 }-> a__U23(2, z', z'', z4) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0 a__U22(z, z', z'', z4) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z4 >= 0 a__U22(z, z', z'', z4) -{ 0 }-> 1 + z + z' + z'' + z4 :|: z' >= 0, z >= 0, z'' >= 0, z4 >= 0 a__U23(z, z', z'', z4) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z4 >= 0 a__U23(z, z', z'', z4) -{ 0 }-> 1 + mark(z4) + (1 + z'' + z') :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0 a__U23(z, z', z'', z4) -{ 0 }-> 1 + z + z' + z'' + z4 :|: z' >= 0, z >= 0, z'' >= 0, z4 >= 0 a__length(z) -{ 0 }-> a__U11(2, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> 0 :|: z = 1 a__length(z) -{ 0 }-> 0 :|: z >= 0 a__length(z) -{ 0 }-> 1 + z :|: z >= 0 a__take(z, z') -{ 0 }-> a__U21(2, z2, z - 1, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 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__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(z0365), mark(z1284))) :|: z = 1 + (1 + z0365 + z1284), z0365 >= 0, z1284 >= 0 mark(z) -{ 0 }-> a__length(a__length(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__length(a__U23(mark(z0364), z1283, z2121, z3121)) :|: z2121 >= 0, z1283 >= 0, z = 1 + (1 + z0364 + z1283 + z2121 + z3121), z3121 >= 0, z0364 >= 0 mark(z) -{ 0 }-> a__length(a__U22(mark(z0363), z1282, z2120, z3120)) :|: z = 1 + (1 + z0363 + z1282 + z2120 + z3120), z1282 >= 0, z3120 >= 0, z2120 >= 0, z0363 >= 0 mark(z) -{ 0 }-> a__length(a__U21(mark(z0362), z1281, z2119, z3119)) :|: z2119 >= 0, z1281 >= 0, z3119 >= 0, z = 1 + (1 + z0362 + z1281 + z2119 + z3119), z0362 >= 0 mark(z) -{ 0 }-> a__length(a__U12(mark(z0360), z1280)) :|: z = 1 + (1 + z0360 + z1280), z0360 >= 0, z1280 >= 0 mark(z) -{ 0 }-> a__length(a__U11(mark(z0359), z1279)) :|: z = 1 + (1 + z0359 + z1279), z0359 >= 0, z1279 >= 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(z0366) + z1285) :|: z1285 >= 0, z0366 >= 0, z = 1 + (1 + z0366 + z1285) mark(z) -{ 0 }-> a__length(1 + 0 + 3) :|: z = 1 + 3 mark(z) -{ 0 }-> a__U23(a__take(mark(z0392), mark(z1305)), z1, z2, z3) :|: z1305 >= 0, z1 >= 0, z0392 >= 0, z = 1 + (1 + z0392 + z1305) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__length(mark(z0388)), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0388) + z1 + z2 + z3, z0388 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__U23(mark(z0391), z1304, z2130, z3130), z1, z2, z3) :|: z3130 >= 0, z1304 >= 0, z1 >= 0, z = 1 + (1 + z0391 + z1304 + z2130 + z3130) + z1 + z2 + z3, z2130 >= 0, z0391 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__U22(mark(z0390), z1303, z2129, z3129), z1, z2, z3) :|: z2129 >= 0, z1 >= 0, z = 1 + (1 + z0390 + z1303 + z2129 + z3129) + z1 + z2 + z3, z0390 >= 0, z1303 >= 0, z3129 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__U21(mark(z0389), z1302, z2128, z3128), z1, z2, z3) :|: z3128 >= 0, z1 >= 0, z1302 >= 0, z2128 >= 0, z = 1 + (1 + z0389 + z1302 + z2128 + z3128) + z1 + z2 + z3, z0389 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__U12(mark(z0387), z1301), z1, z2, z3) :|: z1301 >= 0, z1 >= 0, z0387 >= 0, z = 1 + (1 + z0387 + z1301) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(a__U11(mark(z0386), z1300), z1, z2, z3) :|: z = 1 + (1 + z0386 + z1300) + z1 + z2 + z3, z0386 >= 0, z1300 >= 0, z1 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(3, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(2, z1, z2, z3) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(1, z1, z2, z3) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(0, z1, z2, z3) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(0, z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(0, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(1 + mark(z0394), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0394) + z1 + z2 + z3, z0394 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U23(1 + mark(z0393) + z1306, z1, z2, z3) :|: z = 1 + (1 + z0393 + z1306) + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0, z0393 >= 0, z1306 >= 0 mark(z) -{ 0 }-> a__U23(1 + 0 + 3, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(a__take(mark(z0383), mark(z1298)), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0383 + z1298) + z1 + z2 + z3, z1298 >= 0, z2 >= 0, z3 >= 0, z0383 >= 0 mark(z) -{ 0 }-> a__U22(a__length(mark(z0379)), z1, z2, z3) :|: z = 1 + (1 + z0379) + z1 + z2 + z3, z1 >= 0, z0379 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(a__U23(mark(z0382), z1297, z2127, z3127), z1, z2, z3) :|: z0382 >= 0, z1 >= 0, z2127 >= 0, z = 1 + (1 + z0382 + z1297 + z2127 + z3127) + z1 + z2 + z3, z3127 >= 0, z2 >= 0, z3 >= 0, z1297 >= 0 mark(z) -{ 0 }-> a__U22(a__U22(mark(z0381), z1296, z2126, z3126), z1, z2, z3) :|: z1296 >= 0, z2126 >= 0, z1 >= 0, z = 1 + (1 + z0381 + z1296 + z2126 + z3126) + z1 + z2 + z3, z0381 >= 0, z3126 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(a__U21(mark(z0380), z1295, z2125, z3125), z1, z2, z3) :|: z2125 >= 0, z1 >= 0, z1295 >= 0, z0380 >= 0, z3125 >= 0, z = 1 + (1 + z0380 + z1295 + z2125 + z3125) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(a__U12(mark(z0378), z1294), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0378 + z1294) + z1 + z2 + z3, z0378 >= 0, z1294 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(a__U11(mark(z0377), z1293), z1, z2, z3) :|: z1 >= 0, z0377 >= 0, z1293 >= 0, z = 1 + (1 + z0377 + z1293) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(3, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(2, z1, z2, z3) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(1, z1, z2, z3) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(0, z1, z2, z3) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(0, z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(0, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(1 + mark(z0385), z1, z2, z3) :|: z1 >= 0, z0385 >= 0, z = 1 + (1 + z0385) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(1 + mark(z0384) + z1299, z1, z2, z3) :|: z1 >= 0, z1299 >= 0, z0384 >= 0, z = 1 + (1 + z0384 + z1299) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(1 + 0 + 3, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(a__take(mark(z0374), mark(z1291)), z1, z2, z3) :|: z1 >= 0, z1291 >= 0, z = 1 + (1 + z0374 + z1291) + z1 + z2 + z3, z0374 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(a__length(mark(z0370)), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0370) + z1 + z2 + z3, z0370 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(a__U23(mark(z0373), z1290, z2124, z3124), z1, z2, z3) :|: z = 1 + (1 + z0373 + z1290 + z2124 + z3124) + z1 + z2 + z3, z3124 >= 0, z1 >= 0, z1290 >= 0, z2124 >= 0, z2 >= 0, z3 >= 0, z0373 >= 0 mark(z) -{ 0 }-> a__U21(a__U22(mark(z0372), z1289, z2123, z3123), z1, z2, z3) :|: z0372 >= 0, z1 >= 0, z1289 >= 0, z3123 >= 0, z = 1 + (1 + z0372 + z1289 + z2123 + z3123) + z1 + z2 + z3, z2123 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(a__U21(mark(z0371), z1288, z2122, z3122), z1, z2, z3) :|: z2122 >= 0, z1 >= 0, z0371 >= 0, z3122 >= 0, z = 1 + (1 + z0371 + z1288 + z2122 + z3122) + z1 + z2 + z3, z1288 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(a__U12(mark(z0369), z1287), z1, z2, z3) :|: z1 >= 0, z0369 >= 0, z = 1 + (1 + z0369 + z1287) + z1 + z2 + z3, z2 >= 0, z3 >= 0, z1287 >= 0 mark(z) -{ 0 }-> a__U21(a__U11(mark(z0368), z1286), z1, z2, z3) :|: z1 >= 0, z = 1 + (1 + z0368 + z1286) + z1 + z2 + z3, z0368 >= 0, z1286 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(3, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(2, z1, z2, z3) :|: z1 >= 0, z = 1 + 2 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(1, z1, z2, z3) :|: z = 1 + 1 + z1 + z2 + z3, z1 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(0, z1, z2, z3) :|: z1 >= 0, z = 1 + 0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(0, z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(0, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(1 + mark(z0376), z1, z2, z3) :|: z0376 >= 0, z1 >= 0, z = 1 + (1 + z0376) + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(1 + mark(z0375) + z1292, z1, z2, z3) :|: z1292 >= 0, z = 1 + (1 + z0375 + z1292) + z1 + z2 + z3, z1 >= 0, z0375 >= 0, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(1 + 0 + 3, z1, z2, z3) :|: z1 >= 0, z = 1 + 3 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U12(a__take(mark(z0356), mark(z1277)), z1) :|: z1 >= 0, z = 1 + (1 + z0356 + z1277) + z1, z0356 >= 0, z1277 >= 0 mark(z) -{ 0 }-> a__U12(a__length(mark(z0352)), z1) :|: z1 >= 0, z = 1 + (1 + z0352) + z1, z0352 >= 0 mark(z) -{ 0 }-> a__U12(a__U23(mark(z0355), z1276, z2118, z3118), z1) :|: z = 1 + (1 + z0355 + z1276 + z2118 + z3118) + z1, z1 >= 0, z0355 >= 0, z2118 >= 0, z3118 >= 0, z1276 >= 0 mark(z) -{ 0 }-> a__U12(a__U22(mark(z0354), z1275, z2117, z3117), z1) :|: z3117 >= 0, z1 >= 0, z1275 >= 0, z = 1 + (1 + z0354 + z1275 + z2117 + z3117) + z1, z2117 >= 0, z0354 >= 0 mark(z) -{ 0 }-> a__U12(a__U21(mark(z0353), z1274, z2116, z3116), z1) :|: z1 >= 0, z2116 >= 0, z1274 >= 0, z = 1 + (1 + z0353 + z1274 + z2116 + z3116) + z1, z3116 >= 0, z0353 >= 0 mark(z) -{ 0 }-> a__U12(a__U12(mark(z0351), z1273), z1) :|: z1 >= 0, z = 1 + (1 + z0351 + z1273) + z1, z0351 >= 0, z1273 >= 0 mark(z) -{ 0 }-> a__U12(a__U11(mark(z0350), z1272), z1) :|: z1 >= 0, z0350 >= 0, z1272 >= 0, z = 1 + (1 + z0350 + z1272) + z1 mark(z) -{ 0 }-> a__U12(3, z - 4) :|: z - 4 >= 0 mark(z) -{ 0 }-> a__U12(2, z - 3) :|: z - 3 >= 0 mark(z) -{ 0 }-> a__U12(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__U12(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U12(0, z - 4) :|: z - 4 >= 0 mark(z) -{ 0 }-> a__U12(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U12(1 + mark(z0358), z1) :|: z1 >= 0, z = 1 + (1 + z0358) + z1, z0358 >= 0 mark(z) -{ 0 }-> a__U12(1 + mark(z0357) + z1278, z1) :|: z = 1 + (1 + z0357 + z1278) + z1, z1 >= 0, z0357 >= 0, z1278 >= 0 mark(z) -{ 0 }-> a__U12(1 + 0 + 3, z - 4) :|: z - 4 >= 0 mark(z) -{ 0 }-> a__U11(a__take(mark(z0347), mark(z1270)), z1) :|: z1 >= 0, z0347 >= 0, z1270 >= 0, z = 1 + (1 + z0347 + z1270) + z1 mark(z) -{ 0 }-> a__U11(a__length(mark(z0343)), z1) :|: z1 >= 0, z = 1 + (1 + z0343) + z1, z0343 >= 0 mark(z) -{ 0 }-> a__U11(a__U23(mark(z0346), z1269, z2115, z3115), z1) :|: z2115 >= 0, z1 >= 0, z1269 >= 0, z3115 >= 0, z0346 >= 0, z = 1 + (1 + z0346 + z1269 + z2115 + z3115) + z1 mark(z) -{ 0 }-> a__U11(a__U22(mark(z0345), z1268, z2114, z3114), z1) :|: z1268 >= 0, z1 >= 0, z0345 >= 0, z = 1 + (1 + z0345 + z1268 + z2114 + z3114) + z1, z3114 >= 0, z2114 >= 0 mark(z) -{ 0 }-> a__U11(a__U21(mark(z0344), z1267, z2113, z3113), z1) :|: z3113 >= 0, z0344 >= 0, z1 >= 0, z2113 >= 0, z = 1 + (1 + z0344 + z1267 + z2113 + z3113) + z1, z1267 >= 0 mark(z) -{ 0 }-> a__U11(a__U12(mark(z0342), z1266), z1) :|: z1 >= 0, z = 1 + (1 + z0342 + z1266) + z1, z0342 >= 0, z1266 >= 0 mark(z) -{ 0 }-> a__U11(a__U11(mark(z0341), z1265), z1) :|: z = 1 + (1 + z0341 + z1265) + z1, z0341 >= 0, z1 >= 0, z1265 >= 0 mark(z) -{ 0 }-> a__U11(3, z - 4) :|: z - 4 >= 0 mark(z) -{ 0 }-> a__U11(2, z - 3) :|: z - 3 >= 0 mark(z) -{ 0 }-> a__U11(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__U11(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U11(0, z - 4) :|: z - 4 >= 0 mark(z) -{ 0 }-> a__U11(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U11(1 + mark(z0349), z1) :|: z1 >= 0, z0349 >= 0, z = 1 + (1 + z0349) + z1 mark(z) -{ 0 }-> a__U11(1 + mark(z0348) + z1271, z1) :|: z1271 >= 0, z0348 >= 0, z1 >= 0, z = 1 + (1 + z0348 + z1271) + z1 mark(z) -{ 0 }-> a__U11(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__U11(v0, v1) -> null_a__U11 [0] a__U12(v0, v1) -> null_a__U12 [0] a__U21(v0, v1, v2, v3) -> null_a__U21 [0] a__U22(v0, v1, v2, v3) -> null_a__U22 [0] a__U23(v0, v1, v2, v3) -> null_a__U23 [0] a__length(v0) -> null_a__length [0] a__take(v0, v1) -> null_a__take [0] mark(v0) -> null_mark [0] A__U11(v0, v1) -> null_A__U11 [0] A__U12(v0, v1) -> null_A__U12 [0] A__U21(v0, v1, v2, v3) -> null_A__U21 [0] A__U22(v0, v1, v2, v3) -> null_A__U22 [0] A__U23(v0, v1, v2, v3) -> null_A__U23 [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__U11, null_a__U12, null_a__U21, null_a__U22, null_a__U23, null_a__length, null_a__take, null_mark, null_A__U11, null_A__U12, null_A__U21, null_A__U22, null_A__U23, 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__U11(tt, z0) -> c2(A__U12(tt, z0)) [1] A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) [1] A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) [1] A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) [1] A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) [1] A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) [1] MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) [1] MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) [1] MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c27(MARK(z0)) [1] MARK(s(z0)) -> c30(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__U11(tt, z0) -> a__U12(tt, z0) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U12(tt, z0) -> s(a__length(mark(z0))) [0] a__U12(z0, z1) -> U12(z0, z1) [0] a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) [0] a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) [0] a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) [0] a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) [0] a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) [0] a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) [0] a__length(nil) -> 0 [0] a__length(cons(z0, z1)) -> a__U11(tt, z1) [0] a__length(z0) -> length(z0) [0] a__take(0, z0) -> nil [0] a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) [0] a__take(z0, z1) -> take(z0, z1) [0] mark(zeros) -> a__zeros [0] mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0] mark(U12(z0, z1)) -> a__U12(mark(z0), z1) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) [0] mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) [0] mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) [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(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] a__zeros -> null_a__zeros [0] a__U11(v0, v1) -> null_a__U11 [0] a__U12(v0, v1) -> null_a__U12 [0] a__U21(v0, v1, v2, v3) -> null_a__U21 [0] a__U22(v0, v1, v2, v3) -> null_a__U22 [0] a__U23(v0, v1, v2, v3) -> null_a__U23 [0] a__length(v0) -> null_a__length [0] a__take(v0, v1) -> null_a__take [0] mark(v0) -> null_mark [0] A__U11(v0, v1) -> null_A__U11 [0] A__U12(v0, v1) -> null_A__U12 [0] A__U21(v0, v1, v2, v3) -> null_A__U21 [0] A__U22(v0, v1, v2, v3) -> null_A__U22 [0] A__U23(v0, v1, v2, v3) -> null_A__U23 [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__U11 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c2:null_A__U11 tt :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c2 :: c4:null_A__U12 -> c2:null_A__U11 A__U12 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c4:null_A__U12 c4 :: c13:null_A__LENGTH -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK -> c4:null_A__U12 A__LENGTH :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c13:null_A__LENGTH mark :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark MARK :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK A__U21 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c6:null_A__U21 c6 :: c8:null_A__U22 -> c6:null_A__U21 A__U22 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c8:null_A__U22 c8 :: c10:null_A__U23 -> c8:null_A__U22 A__U23 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c10:null_A__U23 c10 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK -> c10:null_A__U23 cons :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c13 :: c2:null_A__U11 -> c13:null_A__LENGTH A__TAKE :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> c16:null_A__TAKE s :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c16 :: c6:null_A__U21 -> c16:null_A__TAKE U11 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c19 :: c2:null_A__U11 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK U12 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c20 :: c4:null_A__U12 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK length :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c21 :: c13:null_A__LENGTH -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK U21 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c22 :: c6:null_A__U21 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK U22 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c23 :: c8:null_A__U22 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK U23 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c24 :: c10:null_A__U23 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK take :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark c25 :: c16:null_A__TAKE -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK c26 :: c16:null_A__TAKE -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK c27 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK c30 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c30:null_MARK a__zeros :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark 0 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark zeros :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__U11 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__U12 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__length :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__U21 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__U22 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__U23 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark nil :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark a__take :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark -> tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__zeros :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__U11 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__U12 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__U21 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__U22 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__U23 :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__length :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_a__take :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_mark :: tt:cons:s:U11:U12:length:U21:U22:U23:take:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U23:null_a__length:null_a__take:null_mark null_A__U11 :: c2:null_A__U11 null_A__U12 :: c4:null_A__U12 null_A__U21 :: c6:null_A__U21 null_A__U22 :: c8:null_A__U22 null_A__U23 :: c10:null_A__U23 null_A__LENGTH :: c13:null_A__LENGTH null_A__TAKE :: c16:null_A__TAKE null_MARK :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c30: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__U11 => 0 null_a__U12 => 0 null_a__U21 => 0 null_a__U22 => 0 null_a__U23 => 0 null_a__length => 0 null_a__take => 0 null_mark => 0 null_A__U11 => 0 null_A__U12 => 0 null_A__U21 => 0 null_A__U22 => 0 null_A__U23 => 0 null_A__LENGTH => 0 null_A__TAKE => 0 null_MARK => 0 ---------------------------------------- (48) Obligation: Complexity RNTS consisting of the following rules: A__LENGTH(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__LENGTH(z) -{ 1 }-> 1 + A__U11(2, 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 + A__U21(2, z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U11(z, z') -{ 1 }-> 1 + A__U12(2, z0) :|: z = 2, z0 >= 0, z' = z0 A__U12(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U12(z, z') -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 2, z0 >= 0, z' = z0 A__U21(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 A__U21(z, z', z'', z4) -{ 1 }-> 1 + A__U22(2, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 A__U22(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 A__U22(z, z', z'', z4) -{ 1 }-> 1 + A__U23(2, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 A__U23(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 A__U23(z, z', z'', z4) -{ 1 }-> 1 + MARK(z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 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__U23(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U22(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 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 a__U11(z, z') -{ 0 }-> a__U12(2, z0) :|: z = 2, z0 >= 0, z' = z0 a__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U11(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U12(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U12(z, z') -{ 0 }-> 1 + a__length(mark(z0)) :|: z = 2, z0 >= 0, z' = z0 a__U12(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U21(z, z', z'', z4) -{ 0 }-> a__U22(2, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U21(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U21(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__U22(z, z', z'', z4) -{ 0 }-> a__U23(2, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U22(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U22(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__U23(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U23(z, z', z'', z4) -{ 0 }-> 1 + mark(z2) + (1 + z1 + z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U23(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__length(z) -{ 0 }-> a__U11(2, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 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__take(z, z') -{ 0 }-> a__U21(2, z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 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__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__U23(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U22(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U21(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U12(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U11(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__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) by A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros), MARK(zeros)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, 0) -> c4(A__LENGTH(0), MARK(0)) A__U12(tt, tt) -> c4(A__LENGTH(tt), MARK(tt)) A__U12(tt, s(z0)) -> c4(A__LENGTH(s(mark(z0))), MARK(s(z0))) A__U12(tt, nil) -> c4(A__LENGTH(nil), MARK(nil)) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros), MARK(zeros)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, 0) -> c4(A__LENGTH(0), MARK(0)) A__U12(tt, tt) -> c4(A__LENGTH(tt), MARK(tt)) A__U12(tt, s(z0)) -> c4(A__LENGTH(s(mark(z0))), MARK(s(z0))) A__U12(tt, nil) -> c4(A__LENGTH(nil), MARK(nil)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros), MARK(zeros)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, 0) -> c4(A__LENGTH(0), MARK(0)) A__U12(tt, tt) -> c4(A__LENGTH(tt), MARK(tt)) A__U12(tt, s(z0)) -> c4(A__LENGTH(s(mark(z0))), MARK(s(z0))) A__U12(tt, nil) -> c4(A__LENGTH(nil), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2 ---------------------------------------- (51) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: A__U12(tt, nil) -> c4(A__LENGTH(nil), MARK(nil)) A__U12(tt, 0) -> c4(A__LENGTH(0), MARK(0)) A__U12(tt, tt) -> c4(A__LENGTH(tt), MARK(tt)) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros), MARK(zeros)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros), MARK(zeros)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_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__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) by MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(cons(z0, z1), x1)) -> c19(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(0, x1)) -> c19(A__U11(0, x1), MARK(0)) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c19(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(nil, x1)) -> c19(A__U11(nil, x1), MARK(nil)) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(cons(z0, z1), x1)) -> c19(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(0, x1)) -> c19(A__U11(0, x1), MARK(0)) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c19(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(nil, x1)) -> c19(A__U11(nil, x1), MARK(nil)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(cons(z0, z1), x1)) -> c19(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(0, x1)) -> c19(A__U11(0, x1), MARK(0)) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c19(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(nil, x1)) -> c19(A__U11(nil, x1), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2 ---------------------------------------- (57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U11(0, x1)) -> c19(A__U11(0, x1), MARK(0)) MARK(U11(nil, x1)) -> c19(A__U11(nil, x1), MARK(nil)) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(cons(z0, z1), x1)) -> c19(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c19(A__U11(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(cons(z0, z1), x1)) -> c19(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c19(A__U11(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_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__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) by MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1), MARK(zeros)) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(cons(z0, z1), x1)) -> c20(A__U12(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U12(0, x1)) -> c20(A__U12(0, x1), MARK(0)) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c20(A__U12(s(mark(z0)), x1), MARK(s(z0))) MARK(U12(nil, x1)) -> c20(A__U12(nil, x1), MARK(nil)) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1), MARK(zeros)) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(cons(z0, z1), x1)) -> c20(A__U12(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U12(0, x1)) -> c20(A__U12(0, x1), MARK(0)) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c20(A__U12(s(mark(z0)), x1), MARK(s(z0))) MARK(U12(nil, x1)) -> c20(A__U12(nil, x1), MARK(nil)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1), MARK(zeros)) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(cons(z0, z1), x1)) -> c20(A__U12(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U12(0, x1)) -> c20(A__U12(0, x1), MARK(0)) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c20(A__U12(s(mark(z0)), x1), MARK(s(z0))) MARK(U12(nil, x1)) -> c20(A__U12(nil, x1), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2 ---------------------------------------- (63) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U12(nil, x1)) -> c20(A__U12(nil, x1), MARK(nil)) MARK(U12(0, x1)) -> c20(A__U12(0, x1), MARK(0)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1), MARK(zeros)) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(cons(z0, z1), x1)) -> c20(A__U12(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c20(A__U12(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1), MARK(zeros)) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(cons(z0, z1), x1)) -> c20(A__U12(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c20(A__U12(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) by MARK(length(zeros)) -> c21(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c21(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c21(A__LENGTH(tt), MARK(tt)) MARK(length(s(z0))) -> c21(A__LENGTH(s(mark(z0))), MARK(s(z0))) MARK(length(nil)) -> c21(A__LENGTH(nil), MARK(nil)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c21(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c21(A__LENGTH(tt), MARK(tt)) MARK(length(s(z0))) -> c21(A__LENGTH(s(mark(z0))), MARK(s(z0))) MARK(length(nil)) -> c21(A__LENGTH(nil), MARK(nil)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c21(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c21(A__LENGTH(tt), MARK(tt)) MARK(length(s(z0))) -> c21(A__LENGTH(s(mark(z0))), MARK(s(z0))) MARK(length(nil)) -> c21(A__LENGTH(nil), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2 ---------------------------------------- (69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(length(0)) -> c21(A__LENGTH(0), MARK(0)) MARK(length(nil)) -> c21(A__LENGTH(nil), MARK(nil)) MARK(length(tt)) -> c21(A__LENGTH(tt), MARK(tt)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) by MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(A__U21(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U21(0, x1, x2, x3)) -> c22(A__U21(0, x1, x2, x3), MARK(0)) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3), MARK(tt)) MARK(U21(s(z0), x1, x2, x3)) -> c22(A__U21(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U21(nil, x1, x2, x3)) -> c22(A__U21(nil, x1, x2, x3), MARK(nil)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(A__U21(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U21(0, x1, x2, x3)) -> c22(A__U21(0, x1, x2, x3), MARK(0)) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3), MARK(tt)) MARK(U21(s(z0), x1, x2, x3)) -> c22(A__U21(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U21(nil, x1, x2, x3)) -> c22(A__U21(nil, x1, x2, x3), MARK(nil)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(A__U21(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U21(0, x1, x2, x3)) -> c22(A__U21(0, x1, x2, x3), MARK(0)) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3), MARK(tt)) MARK(U21(s(z0), x1, x2, x3)) -> c22(A__U21(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U21(nil, x1, x2, x3)) -> c22(A__U21(nil, x1, x2, x3), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2 ---------------------------------------- (75) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U21(nil, x1, x2, x3)) -> c22(A__U21(nil, x1, x2, x3), MARK(nil)) MARK(U21(0, x1, x2, x3)) -> c22(A__U21(0, x1, x2, x3), MARK(0)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(A__U21(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3), MARK(tt)) MARK(U21(s(z0), x1, x2, x3)) -> c22(A__U21(s(mark(z0)), x1, x2, x3), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(A__U21(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3), MARK(tt)) MARK(U21(s(z0), x1, x2, x3)) -> c22(A__U21(s(mark(z0)), x1, x2, x3), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) by MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(A__U22(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U22(0, x1, x2, x3)) -> c23(A__U22(0, x1, x2, x3), MARK(0)) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3), MARK(tt)) MARK(U22(s(z0), x1, x2, x3)) -> c23(A__U22(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U22(nil, x1, x2, x3)) -> c23(A__U22(nil, x1, x2, x3), MARK(nil)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(A__U22(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U22(0, x1, x2, x3)) -> c23(A__U22(0, x1, x2, x3), MARK(0)) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3), MARK(tt)) MARK(U22(s(z0), x1, x2, x3)) -> c23(A__U22(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U22(nil, x1, x2, x3)) -> c23(A__U22(nil, x1, x2, x3), MARK(nil)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(A__U22(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U22(0, x1, x2, x3)) -> c23(A__U22(0, x1, x2, x3), MARK(0)) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3), MARK(tt)) MARK(U22(s(z0), x1, x2, x3)) -> c23(A__U22(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U22(nil, x1, x2, x3)) -> c23(A__U22(nil, x1, x2, x3), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2 ---------------------------------------- (81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U22(0, x1, x2, x3)) -> c23(A__U22(0, x1, x2, x3), MARK(0)) MARK(U22(nil, x1, x2, x3)) -> c23(A__U22(nil, x1, x2, x3), MARK(nil)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(A__U22(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3), MARK(tt)) MARK(U22(s(z0), x1, x2, x3)) -> c23(A__U22(s(mark(z0)), x1, x2, x3), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(A__U22(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3), MARK(tt)) MARK(U22(s(z0), x1, x2, x3)) -> c23(A__U22(s(mark(z0)), x1, x2, x3), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) by MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(A__U23(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U23(0, x1, x2, x3)) -> c24(A__U23(0, x1, x2, x3), MARK(0)) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3), MARK(tt)) MARK(U23(s(z0), x1, x2, x3)) -> c24(A__U23(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U23(nil, x1, x2, x3)) -> c24(A__U23(nil, x1, x2, x3), MARK(nil)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(A__U23(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U23(0, x1, x2, x3)) -> c24(A__U23(0, x1, x2, x3), MARK(0)) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3), MARK(tt)) MARK(U23(s(z0), x1, x2, x3)) -> c24(A__U23(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U23(nil, x1, x2, x3)) -> c24(A__U23(nil, x1, x2, x3), MARK(nil)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(A__U23(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U23(0, x1, x2, x3)) -> c24(A__U23(0, x1, x2, x3), MARK(0)) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3), MARK(tt)) MARK(U23(s(z0), x1, x2, x3)) -> c24(A__U23(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U23(nil, x1, x2, x3)) -> c24(A__U23(nil, x1, x2, x3), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2 ---------------------------------------- (87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U23(0, x1, x2, x3)) -> c24(A__U23(0, x1, x2, x3), MARK(0)) MARK(U23(nil, x1, x2, x3)) -> c24(A__U23(nil, x1, x2, x3), MARK(nil)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(A__U23(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3), MARK(tt)) MARK(U23(s(z0), x1, x2, x3)) -> c24(A__U23(s(mark(z0)), x1, x2, x3), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(A__U23(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3), MARK(tt)) MARK(U23(s(z0), x1, x2, x3)) -> c24(A__U23(s(mark(z0)), x1, x2, x3), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2 ---------------------------------------- (89) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) by MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c25(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c25(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c25(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c25(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c25(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c25(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c25(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(nil, x1)) -> c25(A__TAKE(nil, mark(x1)), MARK(nil)) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c25(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c25(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c25(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c25(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c25(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c25(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c25(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(nil, x1)) -> c25(A__TAKE(nil, mark(x1)), MARK(nil)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c25(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c25(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c25(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c25(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c25(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c25(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c25(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(nil, x1)) -> c25(A__TAKE(nil, mark(x1)), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2 ---------------------------------------- (93) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(tt, x1)) -> c25(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(nil, x1)) -> c25(A__TAKE(nil, mark(x1)), MARK(nil)) MARK(take(0, x1)) -> c25(A__TAKE(0, mark(x1)), MARK(0)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c25(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c25(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c25(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c25(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c25(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c25(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c25(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c25(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c25(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c25(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) by MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c26(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c26(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, s(z0))) -> c26(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(x0, nil)) -> c26(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c26(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c26(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c26(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c26(A__TAKE(nil, mark(x1)), MARK(x1)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c26(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c26(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, s(z0))) -> c26(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(x0, nil)) -> c26(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c26(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c26(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c26(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c26(A__TAKE(nil, mark(x1)), MARK(x1)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c26(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c26(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, s(z0))) -> c26(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(x0, nil)) -> c26(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c26(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c26(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c26(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c26(A__TAKE(nil, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2 ---------------------------------------- (99) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(x0, tt)) -> c26(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, nil)) -> c26(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(x0, 0)) -> c26(A__TAKE(mark(x0), 0), MARK(0)) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c26(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c26(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c26(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c26(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c26(A__TAKE(nil, mark(x1)), MARK(x1)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c26(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c26(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c26(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c26(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c26(A__TAKE(nil, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2 ---------------------------------------- (101) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) by A__U12(tt, U11(x0, z1)) -> c4(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1))) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(x0, z1)) -> c4(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(x0, z1)) -> c4(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (105) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (107) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) by A__U12(tt, U12(x0, z1)) -> c4(A__LENGTH(U12(mark(x0), z1)), MARK(U12(x0, z1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1)), MARK(U12(0, x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1)), MARK(U12(nil, x1))) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(x0, z1)) -> c4(A__LENGTH(U12(mark(x0), z1)), MARK(U12(x0, z1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1)), MARK(U12(0, x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1)), MARK(U12(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(x0, z1)) -> c4(A__LENGTH(U12(mark(x0), z1)), MARK(U12(x0, z1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1)), MARK(U12(0, x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1)), MARK(U12(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (109) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (111) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) by A__U12(tt, length(x0)) -> c4(A__LENGTH(length(mark(x0))), MARK(length(x0))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0)), MARK(length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt)), MARK(length(tt))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil)), MARK(length(nil))) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(x0)) -> c4(A__LENGTH(length(mark(x0))), MARK(length(x0))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0)), MARK(length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt)), MARK(length(tt))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil)), MARK(length(nil))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, 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U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(x0)) -> c4(A__LENGTH(length(mark(x0))), MARK(length(x0))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0)), MARK(length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt)), MARK(length(tt))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil)), MARK(length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (115) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) by A__U12(tt, U21(x0, z1, z2, z3)) -> c4(A__LENGTH(U21(mark(x0), z1, z2, z3)), MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3)), MARK(U21(0, x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3)), MARK(U21(nil, x1, x2, x3))) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(A__LENGTH(U21(mark(x0), z1, z2, z3)), MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3)), MARK(U21(0, x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3)), MARK(U21(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(A__LENGTH(U21(mark(x0), z1, z2, z3)), MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3)), MARK(U21(0, x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3)), MARK(U21(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (117) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (119) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) by A__U12(tt, U22(x0, z1, z2, z3)) -> c4(A__LENGTH(U22(mark(x0), z1, z2, z3)), MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3)), MARK(U22(0, x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3)), MARK(U22(nil, x1, x2, x3))) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, 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U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(A__LENGTH(U22(mark(x0), z1, z2, z3)), MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3)), MARK(U22(0, x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3)), MARK(U22(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(A__LENGTH(U22(mark(x0), z1, z2, z3)), MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3)), MARK(U22(0, x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3)), MARK(U22(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (121) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), 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U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (123) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) by A__U12(tt, U23(x0, z1, z2, z3)) -> c4(A__LENGTH(U23(mark(x0), z1, z2, z3)), MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3)), MARK(U23(0, x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3)), MARK(U23(nil, x1, x2, x3))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, 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x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(A__LENGTH(U23(mark(x0), z1, z2, z3)), MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3)), MARK(U23(0, x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3)), MARK(U23(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(A__LENGTH(U23(mark(x0), z1, z2, z3)), MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3)), MARK(U23(0, x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3)), MARK(U23(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) 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A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> 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A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) by A__U12(tt, take(x0, x1)) -> c4(A__LENGTH(take(mark(x0), mark(x1))), MARK(take(x0, x1))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, 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-> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, x1)) -> c4(A__LENGTH(take(mark(x0), mark(x1))), MARK(take(x0, x1))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) 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A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, x1)) -> c4(A__LENGTH(take(mark(x0), mark(x1))), MARK(take(x0, x1))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) 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c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), 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U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) by A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) A__U12(tt, zeros) -> c4(A__LENGTH(zeros)) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), 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U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) A__U12(tt, zeros) -> c4(A__LENGTH(zeros)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) 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A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) A__U12(tt, zeros) -> c4(A__LENGTH(zeros)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U12(tt, zeros) -> c4(A__LENGTH(zeros)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) 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U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, 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a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), 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a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (135) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) by MARK(U11(U11(x0, z1), x2)) -> c19(A__U11(U11(mark(x0), z1), x2), MARK(U11(x0, z1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2), MARK(U11(0, x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2), MARK(U11(nil, x1))) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), 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A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(x0, z1), x2)) -> c19(A__U11(U11(mark(x0), z1), x2), MARK(U11(x0, z1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2), MARK(U11(0, x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2), MARK(U11(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), 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U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(x0, z1), x2)) -> c19(A__U11(U11(mark(x0), z1), x2), MARK(U11(x0, z1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2), MARK(U11(0, x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2), MARK(U11(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (137) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> 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c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> 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A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (139) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) by MARK(U11(U12(x0, z1), x2)) -> c19(A__U11(U12(mark(x0), z1), x2), MARK(U12(x0, z1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2), MARK(U12(0, x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2), MARK(U12(nil, x1))) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), 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MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(x0, z1), x2)) -> c19(A__U11(U12(mark(x0), z1), x2), MARK(U12(x0, z1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2), MARK(U12(0, x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2), MARK(U12(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, 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z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(x0, z1), x2)) -> c19(A__U11(U12(mark(x0), z1), x2), MARK(U12(x0, z1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2), MARK(U12(0, x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2), MARK(U12(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, 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MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), 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c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), 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c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (143) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) by MARK(U11(length(x0), x1)) -> c19(A__U11(length(mark(x0)), x1), MARK(length(x0))) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1), MARK(length(0))) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1), MARK(length(tt))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1), MARK(length(nil))) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> 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MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(x0), x1)) -> c19(A__U11(length(mark(x0)), x1), MARK(length(x0))) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1), MARK(length(0))) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1), MARK(length(tt))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1), MARK(length(nil))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, 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c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(x0), x1)) -> c19(A__U11(length(mark(x0)), x1), MARK(length(x0))) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1), MARK(length(0))) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1), MARK(length(tt))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1), MARK(length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (145) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> 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A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> 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U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) by MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(A__U11(U21(mark(x0), z1, z2, z3), x4), MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4), MARK(U21(0, x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4), MARK(U21(nil, x1, x2, x3))) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), 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c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(A__U11(U21(mark(x0), z1, z2, z3), x4), MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4), MARK(U21(0, x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4), MARK(U21(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> 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c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(A__U11(U21(mark(x0), z1, z2, z3), x4), MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4), MARK(U21(0, x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4), MARK(U21(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (149) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), 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MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), 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c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (151) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) by MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(A__U11(U22(mark(x0), z1, z2, z3), x4), MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4), MARK(U22(0, x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4), MARK(U22(nil, x1, x2, x3))) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, 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MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(A__U11(U22(mark(x0), z1, z2, z3), x4), MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4), MARK(U22(0, x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4), MARK(U22(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> 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MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), 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MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(A__U11(U22(mark(x0), z1, z2, z3), x4), MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4), MARK(U22(0, x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4), MARK(U22(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (153) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) 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mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), 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MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (155) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) by MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(A__U11(U23(mark(x0), z1, z2, z3), x4), MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4), MARK(U23(0, x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4), MARK(U23(nil, x1, x2, x3))) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, 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x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(A__U11(U23(mark(x0), z1, z2, z3), x4), MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4), MARK(U23(0, x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4), MARK(U23(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), 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MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(A__U11(U23(mark(x0), z1, z2, z3), x4), MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4), MARK(U23(0, x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4), MARK(U23(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (157) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) 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x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) 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MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (159) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) by MARK(U11(take(x0, x1), x2)) -> c19(A__U11(take(mark(x0), mark(x1)), x2), MARK(take(x0, x1))) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), 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nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> 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MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, x1), x2)) -> c19(A__U11(take(mark(x0), mark(x1)), x2), MARK(take(x0, x1))) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> 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MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, x1), x2)) -> c19(A__U11(take(mark(x0), mark(x1)), x2), MARK(take(x0, x1))) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (161) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> 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x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, 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c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), 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x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (163) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) by MARK(U11(zeros, x0)) -> c19(A__U11(cons(0, zeros), x0)) MARK(U11(zeros, x0)) -> c19(A__U11(zeros, x0)) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) 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x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, 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c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), 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z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) MARK(U11(zeros, x0)) -> c19(A__U11(cons(0, zeros), x0)) MARK(U11(zeros, x0)) -> c19(A__U11(zeros, x0)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), 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c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) 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x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) MARK(U11(zeros, x0)) -> c19(A__U11(cons(0, zeros), x0)) MARK(U11(zeros, x0)) -> c19(A__U11(zeros, x0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (165) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U11(zeros, x0)) -> c19(A__U11(zeros, x0)) MARK(U11(zeros, x0)) -> c19(A__U11(cons(0, zeros), x0)) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), 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MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> 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U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, 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c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, 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MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> 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x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> 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c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (169) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) by MARK(U12(U11(x0, z1), x2)) -> c20(A__U12(U11(mark(x0), z1), x2), MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2), MARK(U11(0, x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2), MARK(U11(nil, x1))) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, 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c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> 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MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2), MARK(U11(0, x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2), MARK(U11(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, 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x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> 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c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> 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MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, 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z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(x0, z1), x2)) -> c20(A__U12(U11(mark(x0), z1), x2), MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2), MARK(U11(0, x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2), MARK(U11(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (171) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), 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c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, 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c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (173) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) by MARK(U12(U12(x0, z1), x2)) -> c20(A__U12(U12(mark(x0), z1), x2), MARK(U12(x0, z1))) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2), MARK(U12(0, x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2), MARK(U12(nil, x1))) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, 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z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(x0, z1), x2)) -> c20(A__U12(U12(mark(x0), z1), x2), MARK(U12(x0, z1))) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2), MARK(U12(0, x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2), MARK(U12(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> 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MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(x0, z1), x2)) -> c20(A__U12(U12(mark(x0), z1), x2), MARK(U12(x0, z1))) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2), MARK(U12(0, x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2), MARK(U12(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (175) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, 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x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), 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A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) 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-> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, 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x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, 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x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (177) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) by MARK(U12(length(x0), x1)) -> c20(A__U12(length(mark(x0)), x1), MARK(length(x0))) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1), MARK(length(0))) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1), MARK(length(tt))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1), MARK(length(nil))) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> 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take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) MARK(U12(length(x0), x1)) -> c20(A__U12(length(mark(x0)), x1), MARK(length(x0))) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1), MARK(length(0))) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1), MARK(length(tt))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1), MARK(length(nil))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), 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MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) MARK(U12(length(x0), x1)) -> c20(A__U12(length(mark(x0)), x1), MARK(length(x0))) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1), MARK(length(0))) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1), MARK(length(tt))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1), MARK(length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (179) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, 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MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, 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mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), 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MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (181) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) by MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(A__U12(U21(mark(x0), z1, z2, z3), x4), MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4), MARK(U21(0, x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4), MARK(U21(nil, x1, x2, x3))) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) 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MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(A__U12(U21(mark(x0), z1, z2, z3), x4), MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4), MARK(U21(0, x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4), MARK(U21(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) 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MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> 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c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) 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MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(A__U12(U21(mark(x0), z1, z2, z3), x4), MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4), MARK(U21(0, x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4), MARK(U21(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), 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MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), 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x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (185) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) by MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(A__U12(U22(mark(x0), z1, z2, z3), x4), MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4), MARK(U22(0, x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4), MARK(U22(nil, x1, x2, x3))) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, 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c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), 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x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(A__U12(U22(mark(x0), z1, z2, z3), x4), MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4), MARK(U22(0, x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4), MARK(U22(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, 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MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(A__U12(U22(mark(x0), z1, z2, z3), x4), MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4), MARK(U22(0, x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4), MARK(U22(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (187) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), 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c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), 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c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, 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MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, 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MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (189) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) by MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(A__U12(U23(mark(x0), z1, z2, z3), x4), MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4), MARK(U23(0, x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4), MARK(U23(nil, x1, x2, x3))) ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> 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A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> 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MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(A__U12(U23(mark(x0), z1, z2, z3), x4), MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4), MARK(U23(0, x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4), MARK(U23(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> 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MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, 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MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(A__U12(U23(mark(x0), z1, z2, z3), x4), MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4), MARK(U23(0, x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4), MARK(U23(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (191) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, 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-> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), 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c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) 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c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), 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z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), 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MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (193) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) by MARK(U12(take(x0, x1), x2)) -> c20(A__U12(take(mark(x0), mark(x1)), x2), MARK(take(x0, x1))) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> 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c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), 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MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (195) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), 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MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> 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x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> 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MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (197) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) by MARK(U12(zeros, x0)) -> c20(A__U12(cons(0, zeros), x0)) MARK(U12(zeros, x0)) -> c20(A__U12(zeros, x0)) ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, 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z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) MARK(U12(zeros, x0)) -> c20(A__U12(cons(0, zeros), x0)) MARK(U12(zeros, x0)) -> c20(A__U12(zeros, x0)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, 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c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, 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x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) MARK(U12(zeros, x0)) -> c20(A__U12(cons(0, zeros), x0)) MARK(U12(zeros, x0)) -> c20(A__U12(zeros, x0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (199) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U12(zeros, x0)) -> c20(A__U12(zeros, x0)) MARK(U12(zeros, x0)) -> c20(A__U12(cons(0, zeros), x0)) ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) 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MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, 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c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) 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-> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), 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z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, 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MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (201) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> 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MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) 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length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), 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MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, 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MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (203) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) by MARK(length(U11(x0, z1))) -> c21(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1))) ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), 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tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> 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c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(x0, z1))) -> c21(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, 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MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> 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c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(x0, z1))) -> c21(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (205) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, 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MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> 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MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, 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z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (207) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) by MARK(length(U12(x0, z1))) -> c21(A__LENGTH(U12(mark(x0), z1)), MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1)), MARK(U12(0, x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1)), MARK(U12(nil, x1))) ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), 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MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(x0, z1))) -> c21(A__LENGTH(U12(mark(x0), z1)), MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1)), MARK(U12(0, x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1)), MARK(U12(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), 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-> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, 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x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, 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MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(x0, z1))) -> c21(A__LENGTH(U12(mark(x0), z1)), MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1)), MARK(U12(0, x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1)), MARK(U12(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (209) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> 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x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, 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MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (211) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) by MARK(length(length(x0))) -> c21(A__LENGTH(length(mark(x0))), MARK(length(x0))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0)), MARK(length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt)), MARK(length(tt))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil)), MARK(length(nil))) ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, 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MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) 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MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), 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c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) MARK(length(length(x0))) -> c21(A__LENGTH(length(mark(x0))), MARK(length(x0))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0)), MARK(length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt)), MARK(length(tt))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil)), MARK(length(nil))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, 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c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) MARK(length(length(x0))) -> c21(A__LENGTH(length(mark(x0))), MARK(length(x0))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0)), MARK(length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt)), MARK(length(tt))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil)), MARK(length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (213) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), 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MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c21(MARK(length(x0))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, 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U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), 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x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c21(MARK(length(x0))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (215) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) by MARK(length(U21(x0, z1, z2, z3))) -> c21(A__LENGTH(U21(mark(x0), z1, z2, z3)), MARK(U21(x0, z1, z2, z3))) MARK(length(U21(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) MARK(length(U21(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(length(U21(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3)), MARK(U21(0, x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3)), MARK(U21(nil, x1, x2, x3))) ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> 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A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) 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MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c21(MARK(length(x0))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil))) MARK(length(U21(x0, z1, z2, z3))) -> c21(A__LENGTH(U21(mark(x0), z1, z2, z3)), MARK(U21(x0, z1, z2, z3))) MARK(length(U21(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) MARK(length(U21(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(length(U21(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3)), MARK(U21(0, x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3)), MARK(U21(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_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__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, 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x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, 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MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), 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x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c21(MARK(length(x0))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil))) MARK(length(U21(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) MARK(length(U21(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(length(U21(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (219) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) by MARK(length(U22(x0, z1, z2, z3))) -> c21(A__LENGTH(U22(mark(x0), z1, z2, z3)), MARK(U22(x0, z1, z2, z3))) MARK(length(U22(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) MARK(length(U22(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3)), MARK(U22(0, x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3)), MARK(U22(nil, x1, x2, x3))) ---------------------------------------- (220) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) 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x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, 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x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, 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x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> 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MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, 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MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3)), MARK(U22(0, x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3)), MARK(U22(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), 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MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), 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MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3)), MARK(U22(0, x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3)), MARK(U22(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (221) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (222) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, 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MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> 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c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), 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a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), 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MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) MARK(length(U22(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) MARK(length(U22(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) 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c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c21(MARK(length(x0))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil))) MARK(length(U21(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) MARK(length(U21(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(length(U21(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) MARK(length(U22(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) MARK(length(U22(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (223) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) by MARK(length(U23(x0, z1, z2, z3))) -> c21(A__LENGTH(U23(mark(x0), z1, z2, z3)), MARK(U23(x0, z1, z2, z3))) MARK(length(U23(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3)), MARK(U23(0, x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3)), MARK(U23(nil, x1, x2, x3))) ---------------------------------------- (224) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) 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MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, 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z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), 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c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> 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c21(A__LENGTH(a__length(nil))) MARK(length(U21(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) MARK(length(U21(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(length(U21(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, 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MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) MARK(length(U23(x0, z1, z2, z3))) -> c21(A__LENGTH(U23(mark(x0), z1, z2, z3)), MARK(U23(x0, z1, z2, z3))) MARK(length(U23(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3)), MARK(U23(0, x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3)), MARK(U23(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), 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MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), 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mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) 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c21(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) MARK(length(U22(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) MARK(length(U22(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) MARK(length(U23(x0, z1, z2, z3))) -> c21(A__LENGTH(U23(mark(x0), z1, z2, z3)), MARK(U23(x0, z1, z2, z3))) MARK(length(U23(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3)), MARK(U23(0, x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3)), MARK(U23(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (225) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (226) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> 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MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) 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x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) MARK(length(U22(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) MARK(length(U22(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) MARK(length(U23(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(x0, z1, z2, z3))) -> c21(MARK(U23(x0, z1, z2, z3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> 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c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) MARK(length(U22(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) MARK(length(U22(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) MARK(length(U23(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(x0, z1, z2, z3))) -> c21(MARK(U23(x0, z1, z2, z3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (227) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) by MARK(length(take(x0, x1))) -> c21(A__LENGTH(take(mark(x0), mark(x1))), MARK(take(x0, x1))) MARK(length(take(x0, zeros))) -> c21(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, U11(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) MARK(length(take(x0, U12(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c21(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(length(take(x0, U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(length(take(x0, U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(length(take(x0, take(z0, z1)))) -> c21(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)))) -> c21(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c21(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c21(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, s(z0)))) -> c21(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(x0, nil))) -> c21(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(zeros, x1))) -> c21(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(U11(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) MARK(length(take(U12(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c21(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(length(take(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(length(take(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(length(take(take(z0, z1), x1))) -> c21(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))) -> c21(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c21(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c21(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) ---------------------------------------- (228) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), 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MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> 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MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), 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MARK(length(take(x0, tt))) -> c21(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, s(z0)))) -> c21(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(x0, nil))) -> c21(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(zeros, x1))) -> c21(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(U11(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) MARK(length(take(U12(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c21(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(length(take(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(length(take(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(length(take(take(z0, z1), x1))) -> c21(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))) -> c21(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c21(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c21(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) 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MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), 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MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, 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MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> 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c21(A__LENGTH(a__length(nil))) MARK(length(U21(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) MARK(length(U21(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(length(U21(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) MARK(length(U22(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) MARK(length(U22(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) MARK(length(U23(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(x0, z1, z2, z3))) -> c21(MARK(U23(x0, z1, z2, z3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3))) MARK(length(take(x0, x1))) -> c21(A__LENGTH(take(mark(x0), mark(x1))), MARK(take(x0, x1))) MARK(length(take(x0, zeros))) -> c21(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, U11(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) MARK(length(take(x0, U12(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c21(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(length(take(x0, U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(length(take(x0, U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(length(take(x0, take(z0, z1)))) -> c21(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)))) -> c21(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c21(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c21(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, s(z0)))) -> c21(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(x0, nil))) -> c21(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(zeros, x1))) -> c21(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(U11(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) MARK(length(take(U12(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c21(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(length(take(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(length(take(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(length(take(take(z0, z1), x1))) -> c21(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))) -> c21(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c21(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c21(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (229) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (230) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> 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c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c21(MARK(length(x0))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil))) MARK(length(U21(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) MARK(length(U21(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(length(U21(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) MARK(length(U22(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) MARK(length(U22(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) MARK(length(U23(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(x0, z1, z2, z3))) -> c21(MARK(U23(x0, z1, z2, z3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3))) MARK(length(take(x0, zeros))) -> c21(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, U11(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) MARK(length(take(x0, U12(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c21(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(length(take(x0, U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(length(take(x0, U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(length(take(x0, take(z0, z1)))) -> c21(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)))) -> c21(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c21(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c21(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, s(z0)))) -> c21(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(x0, nil))) -> c21(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(zeros, x1))) -> c21(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(U11(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) MARK(length(take(U12(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c21(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(length(take(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(length(take(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(length(take(take(z0, z1), x1))) -> c21(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))) -> c21(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c21(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c21(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(x0, x1))) -> c21(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (231) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) by MARK(length(zeros)) -> c21(A__LENGTH(cons(0, zeros))) MARK(length(zeros)) -> c21(A__LENGTH(zeros)) ---------------------------------------- (232) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, 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U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> 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c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(x0, x1))) -> c21(MARK(take(x0, x1))) MARK(length(zeros)) -> c21(A__LENGTH(cons(0, zeros))) MARK(length(zeros)) -> c21(A__LENGTH(zeros)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), 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length(z0)))) -> c21(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(length(take(x0, U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(length(take(x0, U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(length(take(x0, take(z0, z1)))) -> c21(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)))) -> c21(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c21(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c21(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, s(z0)))) -> c21(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(x0, nil))) -> c21(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(zeros, x1))) -> c21(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(U11(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) MARK(length(take(U12(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c21(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(length(take(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(length(take(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(length(take(take(z0, z1), x1))) -> c21(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))) -> c21(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c21(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c21(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(x0, x1))) -> c21(MARK(take(x0, x1))) MARK(length(zeros)) -> c21(A__LENGTH(cons(0, zeros))) MARK(length(zeros)) -> c21(A__LENGTH(zeros)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (233) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(length(zeros)) -> c21(A__LENGTH(zeros)) ---------------------------------------- (234) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, 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x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(x0, x1))) -> c21(MARK(take(x0, x1))) MARK(length(zeros)) -> c21(A__LENGTH(cons(0, zeros))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, 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0))) MARK(length(take(x0, tt))) -> c21(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, s(z0)))) -> c21(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(x0, nil))) -> c21(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(zeros, x1))) -> c21(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(U11(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) MARK(length(take(U12(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c21(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(length(take(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(length(take(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(length(take(take(z0, z1), x1))) -> c21(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))) -> c21(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c21(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c21(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(x0, x1))) -> c21(MARK(take(x0, x1))) MARK(length(zeros)) -> c21(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (235) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) by MARK(U21(U11(x0, z1), x2, x3, x4)) -> c22(A__U21(U11(mark(x0), z1), x2, x3, x4), MARK(U11(x0, z1))) MARK(U21(U11(zeros, x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__zeros, x1), x2, x3, x4), MARK(U11(zeros, x1))) MARK(U21(U11(U11(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U11(mark(z0), z1), x1), x2, x3, x4), MARK(U11(U11(z0, z1), x1))) MARK(U21(U11(U12(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U12(mark(z0), z1), x1), x2, x3, x4), MARK(U11(U12(z0, z1), x1))) MARK(U21(U11(length(z0), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__length(mark(z0)), x1), x2, x3, x4), MARK(U11(length(z0), x1))) MARK(U21(U11(U21(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U21(U11(U22(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U21(U11(U23(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U21(U11(take(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__take(mark(z0), mark(z1)), x1), x2, x3, x4), MARK(U11(take(z0, z1), x1))) MARK(U21(U11(cons(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(cons(mark(z0), z1), x1), x2, x3, x4), MARK(U11(cons(z0, z1), x1))) MARK(U21(U11(0, x1), x2, x3, x4)) -> c22(A__U21(a__U11(0, x1), x2, x3, x4), MARK(U11(0, x1))) MARK(U21(U11(tt, x1), x2, x3, x4)) -> c22(A__U21(a__U11(tt, x1), x2, x3, x4), MARK(U11(tt, x1))) MARK(U21(U11(s(z0), x1), x2, x3, x4)) -> c22(A__U21(a__U11(s(mark(z0)), x1), x2, x3, x4), MARK(U11(s(z0), x1))) MARK(U21(U11(nil, x1), x2, x3, x4)) -> c22(A__U21(a__U11(nil, x1), x2, x3, x4), MARK(U11(nil, x1))) ---------------------------------------- (236) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, 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c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), 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z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(x0, z1, z2, z3))) -> c21(MARK(U23(x0, z1, z2, z3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3))) MARK(length(take(x0, zeros))) -> c21(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, U11(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) MARK(length(take(x0, U12(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c21(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(length(take(x0, U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(length(take(x0, U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(length(take(x0, take(z0, z1)))) -> c21(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)))) -> c21(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c21(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c21(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, s(z0)))) -> c21(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(x0, nil))) -> c21(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(zeros, x1))) -> c21(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(U11(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) MARK(length(take(U12(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c21(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(length(take(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(length(take(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(length(take(take(z0, z1), x1))) -> c21(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))) -> c21(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c21(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c21(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(x0, x1))) -> c21(MARK(take(x0, x1))) MARK(length(zeros)) -> c21(A__LENGTH(cons(0, zeros))) MARK(U21(U11(x0, z1), x2, x3, x4)) -> c22(A__U21(U11(mark(x0), z1), x2, x3, x4), MARK(U11(x0, z1))) MARK(U21(U11(zeros, x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__zeros, x1), x2, x3, x4), MARK(U11(zeros, x1))) MARK(U21(U11(U11(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U11(mark(z0), z1), x1), x2, x3, x4), MARK(U11(U11(z0, z1), x1))) MARK(U21(U11(U12(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U12(mark(z0), z1), x1), x2, x3, x4), MARK(U11(U12(z0, z1), x1))) MARK(U21(U11(length(z0), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__length(mark(z0)), x1), x2, x3, x4), MARK(U11(length(z0), x1))) MARK(U21(U11(U21(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U21(U11(U22(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U21(U11(U23(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U21(U11(take(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__take(mark(z0), mark(z1)), x1), x2, x3, x4), MARK(U11(take(z0, z1), x1))) MARK(U21(U11(cons(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(cons(mark(z0), z1), x1), x2, x3, x4), MARK(U11(cons(z0, z1), x1))) MARK(U21(U11(0, x1), x2, x3, x4)) -> c22(A__U21(a__U11(0, x1), x2, x3, x4), MARK(U11(0, x1))) MARK(U21(U11(tt, x1), x2, x3, x4)) -> c22(A__U21(a__U11(tt, x1), x2, x3, x4), MARK(U11(tt, x1))) MARK(U21(U11(s(z0), x1), x2, x3, x4)) -> c22(A__U21(a__U11(s(mark(z0)), x1), x2, x3, x4), MARK(U11(s(z0), x1))) MARK(U21(U11(nil, x1), x2, x3, x4)) -> c22(A__U21(a__U11(nil, x1), x2, x3, x4), MARK(U11(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> 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-> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), 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MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) MARK(length(U23(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(x0, z1, z2, z3))) -> c21(MARK(U23(x0, z1, z2, z3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3))) MARK(length(take(x0, zeros))) -> c21(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, U11(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) MARK(length(take(x0, U12(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c21(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(length(take(x0, U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(length(take(x0, U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(length(take(x0, take(z0, z1)))) -> c21(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)))) -> c21(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c21(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c21(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, s(z0)))) -> c21(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(x0, nil))) -> c21(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(zeros, x1))) -> c21(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(U11(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) MARK(length(take(U12(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c21(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(length(take(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(length(take(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(length(take(take(z0, z1), x1))) -> c21(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))) -> c21(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c21(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c21(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(x0, x1))) -> c21(MARK(take(x0, x1))) MARK(length(zeros)) -> c21(A__LENGTH(cons(0, zeros))) MARK(U21(U11(x0, z1), x2, x3, x4)) -> c22(A__U21(U11(mark(x0), z1), x2, x3, x4), MARK(U11(x0, z1))) MARK(U21(U11(zeros, x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__zeros, x1), x2, x3, x4), MARK(U11(zeros, x1))) MARK(U21(U11(U11(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U11(mark(z0), z1), x1), x2, x3, x4), MARK(U11(U11(z0, z1), x1))) MARK(U21(U11(U12(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U12(mark(z0), z1), x1), x2, x3, x4), MARK(U11(U12(z0, z1), x1))) MARK(U21(U11(length(z0), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__length(mark(z0)), x1), x2, x3, x4), MARK(U11(length(z0), x1))) MARK(U21(U11(U21(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U21(U11(U22(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U21(U11(U23(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U21(U11(take(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__take(mark(z0), mark(z1)), x1), x2, x3, x4), MARK(U11(take(z0, z1), x1))) MARK(U21(U11(cons(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(cons(mark(z0), z1), x1), x2, x3, x4), MARK(U11(cons(z0, z1), x1))) MARK(U21(U11(0, x1), x2, x3, x4)) -> c22(A__U21(a__U11(0, x1), x2, x3, x4), MARK(U11(0, x1))) MARK(U21(U11(tt, x1), x2, x3, x4)) -> c22(A__U21(a__U11(tt, x1), x2, x3, x4), MARK(U11(tt, x1))) MARK(U21(U11(s(z0), x1), x2, x3, x4)) -> c22(A__U21(a__U11(s(mark(z0)), x1), x2, x3, x4), MARK(U11(s(z0), x1))) MARK(U21(U11(nil, x1), x2, x3, x4)) -> c22(A__U21(a__U11(nil, x1), x2, x3, x4), MARK(U11(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (237) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (238) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> 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c22(A__U21(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U21(U11(U22(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U21(U11(U23(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U21(U11(take(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__take(mark(z0), mark(z1)), x1), x2, x3, x4), MARK(U11(take(z0, z1), x1))) MARK(U21(U11(cons(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(cons(mark(z0), z1), x1), x2, x3, x4), MARK(U11(cons(z0, z1), x1))) MARK(U21(U11(tt, x1), x2, x3, x4)) -> c22(A__U21(a__U11(tt, x1), x2, x3, x4), MARK(U11(tt, x1))) MARK(U21(U11(s(z0), x1), x2, x3, x4)) -> c22(A__U21(a__U11(s(mark(z0)), x1), x2, x3, x4), MARK(U11(s(z0), x1))) MARK(U21(U11(x0, z1), x2, x3, x4)) -> c22(MARK(U11(x0, z1))) MARK(U21(U11(zeros, x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__zeros, x1), x2, x3, x4)) MARK(U21(U11(0, x1), x2, x3, x4)) -> c22(A__U21(a__U11(0, x1), x2, x3, x4)) MARK(U21(U11(nil, x1), x2, x3, x4)) -> c22(A__U21(a__U11(nil, x1), x2, x3, x4)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> 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MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, 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MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> 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z1), x1))) -> c21(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))) -> c21(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c21(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c21(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(x0, x1))) -> c21(MARK(take(x0, x1))) MARK(length(zeros)) -> c21(A__LENGTH(cons(0, zeros))) MARK(U21(U11(U11(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U11(mark(z0), z1), x1), x2, x3, x4), MARK(U11(U11(z0, z1), x1))) MARK(U21(U11(U12(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U12(mark(z0), z1), x1), x2, x3, x4), MARK(U11(U12(z0, z1), x1))) MARK(U21(U11(length(z0), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__length(mark(z0)), x1), x2, x3, x4), MARK(U11(length(z0), x1))) MARK(U21(U11(U21(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U21(U11(U22(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U21(U11(U23(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U21(U11(take(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__take(mark(z0), mark(z1)), x1), x2, x3, x4), MARK(U11(take(z0, z1), x1))) MARK(U21(U11(cons(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(cons(mark(z0), z1), x1), x2, x3, x4), MARK(U11(cons(z0, z1), x1))) MARK(U21(U11(tt, x1), x2, x3, x4)) -> c22(A__U21(a__U11(tt, x1), x2, x3, x4), MARK(U11(tt, x1))) MARK(U21(U11(s(z0), x1), x2, x3, x4)) -> c22(A__U21(a__U11(s(mark(z0)), x1), x2, x3, x4), MARK(U11(s(z0), x1))) MARK(U21(U11(x0, z1), x2, x3, x4)) -> c22(MARK(U11(x0, z1))) MARK(U21(U11(zeros, x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__zeros, x1), x2, x3, x4)) MARK(U21(U11(0, x1), x2, x3, x4)) -> c22(A__U21(a__U11(0, x1), x2, x3, x4)) MARK(U21(U11(nil, x1), x2, x3, x4)) -> c22(A__U21(a__U11(nil, x1), x2, x3, x4)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (239) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (240) 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__U11(tt, L) -> a__U12(tt, L) [1] a__U12(tt, L) -> s(a__length(mark(L))) [1] a__U21(tt, IL, M, N) -> a__U22(tt, IL, M, N) [1] a__U22(tt, IL, M, N) -> a__U23(tt, IL, M, N) [1] a__U23(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U11(tt, L) [1] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> a__U21(tt, IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) [1] mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) [1] mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) [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(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__length(X) -> length(X) [1] a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) [1] a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) [1] a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (241) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (242) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__zeros -> cons(0, zeros) [1] a__U11(tt, L) -> a__U12(tt, L) [1] a__U12(tt, L) -> s(a__length(mark(L))) [1] a__U21(tt, IL, M, N) -> a__U22(tt, IL, M, N) [1] a__U22(tt, IL, M, N) -> a__U23(tt, IL, M, N) [1] a__U23(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U11(tt, L) [1] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> a__U21(tt, IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) [1] mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) [1] mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) [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(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__length(X) -> length(X) [1] a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) [1] a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) [1] a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 cons :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 0 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 zeros :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U11 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 tt :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U12 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 s :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__length :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 mark :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U21 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U22 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U23 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 take :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 nil :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__take :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U11 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U12 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 length :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U21 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U22 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U23 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 Rewrite Strategy: INNERMOST ---------------------------------------- (243) 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 ---------------------------------------- (244) 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__U11(tt, L) -> a__U12(tt, L) [1] a__U12(tt, L) -> s(a__length(mark(L))) [1] a__U21(tt, IL, M, N) -> a__U22(tt, IL, M, N) [1] a__U22(tt, IL, M, N) -> a__U23(tt, IL, M, N) [1] a__U23(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U11(tt, L) [1] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> a__U21(tt, IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) [1] mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) [1] mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) [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(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__length(X) -> length(X) [1] a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) [1] a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) [1] a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 cons :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 0 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 zeros :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U11 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 tt :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U12 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 s :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__length :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 mark :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U21 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U22 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U23 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 take :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 nil :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__take :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U11 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U12 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 length :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U21 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U22 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U23 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 Rewrite Strategy: INNERMOST ---------------------------------------- (245) 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 ---------------------------------------- (246) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z') -{ 1 }-> a__U12(2, L) :|: z = 2, L >= 0, z' = L a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U12(z, z') -{ 1 }-> 1 + a__length(mark(L)) :|: z = 2, L >= 0, z' = L a__U12(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U21(z, z', z'', z1) -{ 1 }-> a__U22(2, IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U21(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U22(z, z', z'', z1) -{ 1 }-> a__U23(2, IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U22(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U23(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U23(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__length(z) -{ 1 }-> a__U11(2, L) :|: z = 1 + N + L, L >= 0, N >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__take(z, z') -{ 1 }-> a__U21(2, IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, 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__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__U23(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U22(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U21(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U12(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U11(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. ---------------------------------------- (247) 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__U21_4 a__length_1 a__U22_4 a__U23_4 a__U12_2 a__take_2 a__U11_2 a__zeros Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (248) 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__U11(tt, L) -> a__U12(tt, L) [1] a__U12(tt, L) -> s(a__length(mark(L))) [1] a__U21(tt, IL, M, N) -> a__U22(tt, IL, M, N) [1] a__U22(tt, IL, M, N) -> a__U23(tt, IL, M, N) [1] a__U23(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U11(tt, L) [1] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> a__U21(tt, IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) [1] mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) [1] mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) [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(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__length(X) -> length(X) [1] a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) [1] a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) [1] a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 cons :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 0 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 zeros :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U11 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 tt :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U12 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 s :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__length :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 mark :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U21 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U22 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U23 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 take :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 nil :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__take :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U11 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U12 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 length :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U21 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U22 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U23 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 Rewrite Strategy: INNERMOST ---------------------------------------- (249) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (250) 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__U11(tt, L) -> a__U12(tt, L) [1] a__U12(tt, zeros) -> s(a__length(a__zeros)) [2] a__U12(tt, U11(X1', X2')) -> s(a__length(a__U11(mark(X1'), X2'))) [2] a__U12(tt, U12(X1'', X2'')) -> s(a__length(a__U12(mark(X1''), X2''))) [2] a__U12(tt, length(X')) -> s(a__length(a__length(mark(X')))) [2] a__U12(tt, U21(X11, X21, X3', X4')) -> s(a__length(a__U21(mark(X11), X21, X3', X4'))) [2] a__U12(tt, U22(X12, X22, X3'', X4'')) -> s(a__length(a__U22(mark(X12), X22, X3'', X4''))) [2] a__U12(tt, U23(X13, X23, X31, X41)) -> s(a__length(a__U23(mark(X13), X23, X31, X41))) [2] a__U12(tt, take(X14, X24)) -> s(a__length(a__take(mark(X14), mark(X24)))) [2] a__U12(tt, cons(X15, X25)) -> s(a__length(cons(mark(X15), X25))) [2] a__U12(tt, 0) -> s(a__length(0)) [2] a__U12(tt, tt) -> s(a__length(tt)) [2] a__U12(tt, s(X'')) -> s(a__length(s(mark(X'')))) [2] a__U12(tt, nil) -> s(a__length(nil)) [2] a__U21(tt, IL, M, N) -> a__U22(tt, IL, M, N) [1] a__U22(tt, IL, M, N) -> a__U23(tt, IL, M, N) [1] a__U23(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U11(tt, L) [1] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> a__U21(tt, IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(zeros, X2)) -> a__U11(a__zeros, X2) [2] mark(U11(U11(X16, X26), X2)) -> a__U11(a__U11(mark(X16), X26), X2) [2] mark(U11(U12(X17, X27), X2)) -> a__U11(a__U12(mark(X17), X27), X2) [2] mark(U11(length(X5), X2)) -> a__U11(a__length(mark(X5)), X2) [2] mark(U11(U21(X18, X28, X32, X42), X2)) -> a__U11(a__U21(mark(X18), X28, X32, X42), X2) [2] mark(U11(U22(X19, X29, X33, X43), X2)) -> a__U11(a__U22(mark(X19), X29, X33, X43), X2) [2] mark(U11(U23(X110, X210, X34, X44), X2)) -> a__U11(a__U23(mark(X110), X210, X34, X44), X2) [2] mark(U11(take(X111, X211), X2)) -> a__U11(a__take(mark(X111), mark(X211)), X2) [2] mark(U11(cons(X112, X212), X2)) -> a__U11(cons(mark(X112), X212), X2) [2] mark(U11(0, X2)) -> a__U11(0, X2) [2] mark(U11(tt, X2)) -> a__U11(tt, X2) [2] mark(U11(s(X6), X2)) -> a__U11(s(mark(X6)), X2) [2] mark(U11(nil, X2)) -> a__U11(nil, X2) [2] mark(U12(zeros, X2)) -> a__U12(a__zeros, X2) [2] mark(U12(U11(X113, X213), X2)) -> a__U12(a__U11(mark(X113), X213), X2) [2] mark(U12(U12(X114, X214), X2)) -> a__U12(a__U12(mark(X114), X214), X2) [2] mark(U12(length(X7), X2)) -> a__U12(a__length(mark(X7)), X2) [2] mark(U12(U21(X115, X215, X35, X45), X2)) -> a__U12(a__U21(mark(X115), X215, X35, X45), X2) [2] mark(U12(U22(X116, X216, X36, X46), X2)) -> a__U12(a__U22(mark(X116), X216, X36, X46), X2) [2] mark(U12(U23(X117, X217, X37, X47), X2)) -> a__U12(a__U23(mark(X117), X217, X37, X47), X2) [2] mark(U12(take(X118, X218), X2)) -> a__U12(a__take(mark(X118), mark(X218)), X2) [2] mark(U12(cons(X119, X219), X2)) -> a__U12(cons(mark(X119), X219), X2) [2] mark(U12(0, X2)) -> a__U12(0, X2) [2] mark(U12(tt, X2)) -> a__U12(tt, X2) [2] mark(U12(s(X8), X2)) -> a__U12(s(mark(X8)), X2) [2] mark(U12(nil, X2)) -> a__U12(nil, X2) [2] mark(length(zeros)) -> a__length(a__zeros) [2] mark(length(U11(X120, X220))) -> a__length(a__U11(mark(X120), X220)) [2] mark(length(U12(X121, X221))) -> a__length(a__U12(mark(X121), X221)) [2] mark(length(length(X9))) -> a__length(a__length(mark(X9))) [2] mark(length(U21(X122, X222, X38, X48))) -> a__length(a__U21(mark(X122), X222, X38, X48)) [2] mark(length(U22(X123, X223, X39, X49))) -> a__length(a__U22(mark(X123), X223, X39, X49)) [2] mark(length(U23(X124, X224, X310, X410))) -> a__length(a__U23(mark(X124), X224, X310, X410)) [2] mark(length(take(X125, X225))) -> a__length(a__take(mark(X125), mark(X225))) [2] mark(length(cons(X126, X226))) -> a__length(cons(mark(X126), X226)) [2] mark(length(0)) -> a__length(0) [2] mark(length(tt)) -> a__length(tt) [2] mark(length(s(X10))) -> a__length(s(mark(X10))) [2] mark(length(nil)) -> a__length(nil) [2] mark(U21(zeros, X2, X3, X4)) -> a__U21(a__zeros, X2, X3, X4) [2] mark(U21(U11(X127, X227), X2, X3, X4)) -> a__U21(a__U11(mark(X127), X227), X2, X3, X4) [2] mark(U21(U12(X128, X228), X2, X3, X4)) -> a__U21(a__U12(mark(X128), X228), X2, X3, X4) [2] mark(U21(length(X20), X2, X3, X4)) -> a__U21(a__length(mark(X20)), X2, X3, X4) [2] mark(U21(U21(X129, X229, X311, X411), X2, X3, X4)) -> a__U21(a__U21(mark(X129), X229, X311, X411), X2, X3, X4) [2] mark(U21(U22(X130, X230, X312, X412), X2, X3, X4)) -> a__U21(a__U22(mark(X130), X230, X312, X412), X2, X3, X4) [2] mark(U21(U23(X131, X231, X313, X413), X2, X3, X4)) -> a__U21(a__U23(mark(X131), X231, X313, X413), X2, X3, X4) [2] mark(U21(take(X132, X232), X2, X3, X4)) -> a__U21(a__take(mark(X132), mark(X232)), X2, X3, X4) [2] mark(U21(cons(X133, X233), X2, X3, X4)) -> a__U21(cons(mark(X133), X233), X2, X3, X4) [2] mark(U21(0, X2, X3, X4)) -> a__U21(0, X2, X3, X4) [2] mark(U21(tt, X2, X3, X4)) -> a__U21(tt, X2, X3, X4) [2] mark(U21(s(X30), X2, X3, X4)) -> a__U21(s(mark(X30)), X2, X3, X4) [2] mark(U21(nil, X2, X3, X4)) -> a__U21(nil, X2, X3, X4) [2] mark(U22(zeros, X2, X3, X4)) -> a__U22(a__zeros, X2, X3, X4) [2] mark(U22(U11(X134, X234), X2, X3, X4)) -> a__U22(a__U11(mark(X134), X234), X2, X3, X4) [2] mark(U22(U12(X135, X235), X2, X3, X4)) -> a__U22(a__U12(mark(X135), X235), X2, X3, X4) [2] mark(U22(length(X40), X2, X3, X4)) -> a__U22(a__length(mark(X40)), X2, X3, X4) [2] mark(U22(U21(X136, X236, X314, X414), X2, X3, X4)) -> a__U22(a__U21(mark(X136), X236, X314, X414), X2, X3, X4) [2] mark(U22(U22(X137, X237, X315, X415), X2, X3, X4)) -> a__U22(a__U22(mark(X137), X237, X315, X415), X2, X3, X4) [2] mark(U22(U23(X138, X238, X316, X416), X2, X3, X4)) -> a__U22(a__U23(mark(X138), X238, X316, X416), X2, X3, X4) [2] mark(U22(take(X139, X239), X2, X3, X4)) -> a__U22(a__take(mark(X139), mark(X239)), X2, X3, X4) [2] mark(U22(cons(X140, X240), X2, X3, X4)) -> a__U22(cons(mark(X140), X240), X2, X3, X4) [2] mark(U22(0, X2, X3, X4)) -> a__U22(0, X2, X3, X4) [2] mark(U22(tt, X2, X3, X4)) -> a__U22(tt, X2, X3, X4) [2] mark(U22(s(X50), X2, X3, X4)) -> a__U22(s(mark(X50)), X2, X3, X4) [2] mark(U22(nil, X2, X3, X4)) -> a__U22(nil, X2, X3, X4) [2] mark(U23(zeros, X2, X3, X4)) -> a__U23(a__zeros, X2, X3, X4) [2] mark(U23(U11(X141, X241), X2, X3, X4)) -> a__U23(a__U11(mark(X141), X241), X2, X3, X4) [2] mark(U23(U12(X142, X242), X2, X3, X4)) -> a__U23(a__U12(mark(X142), X242), X2, X3, X4) [2] mark(U23(length(X51), X2, X3, X4)) -> a__U23(a__length(mark(X51)), X2, X3, X4) [2] mark(U23(U21(X143, X243, X317, X417), X2, X3, X4)) -> a__U23(a__U21(mark(X143), X243, X317, X417), X2, X3, X4) [2] mark(U23(U22(X144, X244, X318, X418), X2, X3, X4)) -> a__U23(a__U22(mark(X144), X244, X318, X418), X2, X3, X4) [2] mark(U23(U23(X145, X245, X319, X419), X2, X3, X4)) -> a__U23(a__U23(mark(X145), X245, X319, X419), X2, X3, X4) [2] mark(U23(take(X146, X246), X2, X3, X4)) -> a__U23(a__take(mark(X146), mark(X246)), X2, X3, X4) [2] mark(U23(cons(X147, X247), X2, X3, X4)) -> a__U23(cons(mark(X147), X247), X2, X3, X4) [2] mark(U23(0, X2, X3, X4)) -> a__U23(0, X2, X3, X4) [2] mark(U23(tt, X2, X3, X4)) -> a__U23(tt, X2, X3, X4) [2] mark(U23(s(X52), X2, X3, X4)) -> a__U23(s(mark(X52)), X2, X3, X4) [2] mark(U23(nil, X2, X3, X4)) -> a__U23(nil, X2, X3, X4) [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(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__length(X) -> length(X) [1] a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) [1] a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) [1] a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 cons :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 0 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 zeros :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U11 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 tt :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U12 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 s :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__length :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 mark :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U21 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U22 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U23 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 take :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 nil :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__take :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U11 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U12 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 length :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U21 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U22 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U23 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 Rewrite Strategy: INNERMOST ---------------------------------------- (251) 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 ---------------------------------------- (252) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z') -{ 1 }-> a__U12(2, L) :|: z = 2, L >= 0, z' = L a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U12(z, z') -{ 2 }-> 1 + a__length(a__zeros) :|: z = 2, z' = 3 a__U12(z, z') -{ 2 }-> 1 + a__length(a__take(mark(X14), mark(X24))) :|: z = 2, z' = 1 + X14 + X24, X14 >= 0, X24 >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__length(mark(X'))) :|: z = 2, X' >= 0, z' = 1 + X' a__U12(z, z') -{ 2 }-> 1 + a__length(a__U23(mark(X13), X23, X31, X41)) :|: z = 2, z' = 1 + X13 + X23 + X31 + X41, X31 >= 0, X41 >= 0, X13 >= 0, X23 >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U22(mark(X12), X22, X3'', X4'')) :|: z = 2, X12 >= 0, X22 >= 0, X3'' >= 0, z' = 1 + X12 + X22 + X3'' + X4'', X4'' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U21(mark(X11), X21, X3', X4')) :|: z = 2, X3' >= 0, X4' >= 0, X11 >= 0, X21 >= 0, z' = 1 + X11 + X21 + X3' + X4' a__U12(z, z') -{ 2 }-> 1 + a__length(a__U12(mark(X1''), X2'')) :|: z = 2, z' = 1 + X1'' + X2'', X1'' >= 0, X2'' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U11(mark(X1'), X2')) :|: z = 2, z' = 1 + X1' + X2', X2' >= 0, X1' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(2) :|: z = 2, z' = 2 a__U12(z, z') -{ 2 }-> 1 + a__length(1) :|: z = 2, z' = 1 a__U12(z, z') -{ 2 }-> 1 + a__length(0) :|: z = 2, z' = 0 a__U12(z, z') -{ 2 }-> 1 + a__length(1 + mark(X'')) :|: z = 2, z' = 1 + X'', X'' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(1 + mark(X15) + X25) :|: z = 2, z' = 1 + X15 + X25, X15 >= 0, X25 >= 0 a__U12(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U21(z, z', z'', z1) -{ 1 }-> a__U22(2, IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U21(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U22(z, z', z'', z1) -{ 1 }-> a__U23(2, IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U22(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U23(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U23(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__length(z) -{ 1 }-> a__U11(2, L) :|: z = 1 + N + L, L >= 0, N >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__take(z, z') -{ 1 }-> a__U21(2, IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, 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__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(X125), mark(X225))) :|: X125 >= 0, X225 >= 0, z = 1 + (1 + X125 + X225) mark(z) -{ 2 }-> a__length(a__length(mark(X9))) :|: X9 >= 0, z = 1 + (1 + X9) mark(z) -{ 2 }-> a__length(a__U23(mark(X124), X224, X310, X410)) :|: X124 >= 0, X410 >= 0, X224 >= 0, X310 >= 0, z = 1 + (1 + X124 + X224 + X310 + X410) mark(z) -{ 2 }-> a__length(a__U22(mark(X123), X223, X39, X49)) :|: X223 >= 0, z = 1 + (1 + X123 + X223 + X39 + X49), X49 >= 0, X39 >= 0, X123 >= 0 mark(z) -{ 2 }-> a__length(a__U21(mark(X122), X222, X38, X48)) :|: X222 >= 0, X48 >= 0, X38 >= 0, X122 >= 0, z = 1 + (1 + X122 + X222 + X38 + X48) mark(z) -{ 2 }-> a__length(a__U12(mark(X121), X221)) :|: z = 1 + (1 + X121 + X221), X221 >= 0, X121 >= 0 mark(z) -{ 2 }-> a__length(a__U11(mark(X120), X220)) :|: X120 >= 0, z = 1 + (1 + X120 + X220), X220 >= 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(X10)) :|: z = 1 + (1 + X10), X10 >= 0 mark(z) -{ 2 }-> a__length(1 + mark(X126) + X226) :|: z = 1 + (1 + X126 + X226), X126 >= 0, X226 >= 0 mark(z) -{ 2 }-> a__U23(a__zeros, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__take(mark(X146), mark(X246)), X2, X3, X4) :|: X146 >= 0, z = 1 + (1 + X146 + X246) + X2 + X3 + X4, X246 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__length(mark(X51)), X2, X3, X4) :|: X51 >= 0, z = 1 + (1 + X51) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U23(mark(X145), X245, X319, X419), X2, X3, X4) :|: X319 >= 0, X245 >= 0, X145 >= 0, X419 >= 0, X3 >= 0, z = 1 + (1 + X145 + X245 + X319 + X419) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U22(mark(X144), X244, X318, X418), X2, X3, X4) :|: X244 >= 0, X418 >= 0, X144 >= 0, z = 1 + (1 + X144 + X244 + X318 + X418) + X2 + X3 + X4, X3 >= 0, X318 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U21(mark(X143), X243, X317, X417), X2, X3, X4) :|: X243 >= 0, X3 >= 0, X143 >= 0, X417 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X143 + X243 + X317 + X417) + X2 + X3 + X4, X317 >= 0 mark(z) -{ 2 }-> a__U23(a__U12(mark(X142), X242), X2, X3, X4) :|: X242 >= 0, X3 >= 0, z = 1 + (1 + X142 + X242) + X2 + X3 + X4, X2 >= 0, X4 >= 0, X142 >= 0 mark(z) -{ 2 }-> a__U23(a__U11(mark(X141), X241), X2, X3, X4) :|: z = 1 + (1 + X141 + X241) + X2 + X3 + X4, X3 >= 0, X241 >= 0, X2 >= 0, X4 >= 0, X141 >= 0 mark(z) -{ 2 }-> a__U23(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U23(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U23(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(1 + mark(X52), X2, X3, X4) :|: X3 >= 0, z = 1 + (1 + X52) + X2 + X3 + X4, X52 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(1 + mark(X147) + X247, X2, X3, X4) :|: X147 >= 0, X3 >= 0, z = 1 + (1 + X147 + X247) + X2 + X3 + X4, X247 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__zeros, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__take(mark(X139), mark(X239)), X2, X3, X4) :|: z = 1 + (1 + X139 + X239) + X2 + X3 + X4, X3 >= 0, X239 >= 0, X2 >= 0, X4 >= 0, X139 >= 0 mark(z) -{ 2 }-> a__U22(a__length(mark(X40)), X2, X3, X4) :|: z = 1 + (1 + X40) + X2 + X3 + X4, X40 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__U23(mark(X138), X238, X316, X416), X2, X3, X4) :|: z = 1 + (1 + X138 + X238 + X316 + X416) + X2 + X3 + X4, X3 >= 0, X416 >= 0, X2 >= 0, X4 >= 0, X138 >= 0, X238 >= 0, X316 >= 0 mark(z) -{ 2 }-> a__U22(a__U22(mark(X137), X237, X315, X415), X2, X3, X4) :|: X315 >= 0, z = 1 + (1 + X137 + X237 + X315 + X415) + X2 + X3 + X4, X3 >= 0, X137 >= 0, X2 >= 0, X4 >= 0, X237 >= 0, X415 >= 0 mark(z) -{ 2 }-> a__U22(a__U21(mark(X136), X236, X314, X414), X2, X3, X4) :|: X414 >= 0, X136 >= 0, X3 >= 0, X236 >= 0, X314 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X136 + X236 + X314 + X414) + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(a__U12(mark(X135), X235), X2, X3, X4) :|: X135 >= 0, X3 >= 0, X235 >= 0, z = 1 + (1 + X135 + X235) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__U11(mark(X134), X234), X2, X3, X4) :|: X134 >= 0, X234 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X134 + X234) + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(1 + mark(X50), X2, X3, X4) :|: X50 >= 0, X3 >= 0, z = 1 + (1 + X50) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(1 + mark(X140) + X240, X2, X3, X4) :|: X240 >= 0, z = 1 + (1 + X140 + X240) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0, X140 >= 0 mark(z) -{ 2 }-> a__U21(a__zeros, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__take(mark(X132), mark(X232)), X2, X3, X4) :|: z = 1 + (1 + X132 + X232) + X2 + X3 + X4, X3 >= 0, X232 >= 0, X2 >= 0, X4 >= 0, X132 >= 0 mark(z) -{ 2 }-> a__U21(a__length(mark(X20)), X2, X3, X4) :|: z = 1 + (1 + X20) + X2 + X3 + X4, X20 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U23(mark(X131), X231, X313, X413), X2, X3, X4) :|: X313 >= 0, X3 >= 0, X231 >= 0, X413 >= 0, z = 1 + (1 + X131 + X231 + X313 + X413) + X2 + X3 + X4, X2 >= 0, X4 >= 0, X131 >= 0 mark(z) -{ 2 }-> a__U21(a__U22(mark(X130), X230, X312, X412), X2, X3, X4) :|: z = 1 + (1 + X130 + X230 + X312 + X412) + X2 + X3 + X4, X312 >= 0, X412 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, X130 >= 0, X230 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X129), X229, X311, X411), X2, X3, X4) :|: z = 1 + (1 + X129 + X229 + X311 + X411) + X2 + X3 + X4, X311 >= 0, X411 >= 0, X229 >= 0, X3 >= 0, X129 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U12(mark(X128), X228), X2, X3, X4) :|: X128 >= 0, z = 1 + (1 + X128 + X228) + X2 + X3 + X4, X3 >= 0, X228 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U11(mark(X127), X227), X2, X3, X4) :|: X227 >= 0, X3 >= 0, X127 >= 0, z = 1 + (1 + X127 + X227) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(1 + mark(X30), X2, X3, X4) :|: X30 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X30) + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(1 + mark(X133) + X233, X2, X3, X4) :|: X233 >= 0, X3 >= 0, z = 1 + (1 + X133 + X233) + X2 + X3 + X4, X133 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U12(a__zeros, X2) :|: X2 >= 0, z = 1 + 3 + X2 mark(z) -{ 2 }-> a__U12(a__take(mark(X118), mark(X218)), X2) :|: X118 >= 0, z = 1 + (1 + X118 + X218) + X2, X2 >= 0, X218 >= 0 mark(z) -{ 2 }-> a__U12(a__length(mark(X7)), X2) :|: z = 1 + (1 + X7) + X2, X7 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U23(mark(X117), X217, X37, X47), X2) :|: X47 >= 0, X37 >= 0, X117 >= 0, X2 >= 0, z = 1 + (1 + X117 + X217 + X37 + X47) + X2, X217 >= 0 mark(z) -{ 2 }-> a__U12(a__U22(mark(X116), X216, X36, X46), X2) :|: X216 >= 0, X36 >= 0, z = 1 + (1 + X116 + X216 + X36 + X46) + X2, X116 >= 0, X46 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U21(mark(X115), X215, X35, X45), X2) :|: X115 >= 0, X35 >= 0, X45 >= 0, z = 1 + (1 + X115 + X215 + X35 + X45) + X2, X215 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(X114), X214), X2) :|: X114 >= 0, z = 1 + (1 + X114 + X214) + X2, X214 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X113), X213), X2) :|: X113 >= 0, X213 >= 0, z = 1 + (1 + X113 + X213) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(2, X2) :|: z = 1 + 2 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X8), X2) :|: z = 1 + (1 + X8) + X2, X8 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X119) + X219, X2) :|: z = 1 + (1 + X119 + X219) + X2, X219 >= 0, X2 >= 0, X119 >= 0 mark(z) -{ 2 }-> a__U11(a__zeros, X2) :|: X2 >= 0, z = 1 + 3 + X2 mark(z) -{ 2 }-> a__U11(a__take(mark(X111), mark(X211)), X2) :|: z = 1 + (1 + X111 + X211) + X2, X211 >= 0, X2 >= 0, X111 >= 0 mark(z) -{ 2 }-> a__U11(a__length(mark(X5)), X2) :|: X5 >= 0, z = 1 + (1 + X5) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U23(mark(X110), X210, X34, X44), X2) :|: X110 >= 0, z = 1 + (1 + X110 + X210 + X34 + X44) + X2, X2 >= 0, X210 >= 0, X34 >= 0, X44 >= 0 mark(z) -{ 2 }-> a__U11(a__U22(mark(X19), X29, X33, X43), X2) :|: X33 >= 0, X43 >= 0, X29 >= 0, X19 >= 0, z = 1 + (1 + X19 + X29 + X33 + X43) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X18), X28, X32, X42), X2) :|: X32 >= 0, X18 >= 0, X28 >= 0, z = 1 + (1 + X18 + X28 + X32 + X42) + X2, X42 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X17), X27), X2) :|: X17 >= 0, X27 >= 0, z = 1 + (1 + X17 + X27) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X16), X26), X2) :|: X16 >= 0, X26 >= 0, z = 1 + (1 + X16 + X26) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(2, X2) :|: z = 1 + 2 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X6), X2) :|: X6 >= 0, z = 1 + (1 + X6) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X112) + X212, X2) :|: X212 >= 0, z = 1 + (1 + X112 + X212) + X2, X112 >= 0, X2 >= 0 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (253) 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 :|: ---------------------------------------- (254) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z') -{ 1 }-> a__U12(2, L) :|: z = 2, L >= 0, z' = L a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U12(z, z') -{ 2 }-> 1 + a__length(a__take(mark(X14), mark(X24))) :|: z = 2, z' = 1 + X14 + X24, X14 >= 0, X24 >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__length(mark(X'))) :|: z = 2, X' >= 0, z' = 1 + X' a__U12(z, z') -{ 2 }-> 1 + a__length(a__U23(mark(X13), X23, X31, X41)) :|: z = 2, z' = 1 + X13 + X23 + X31 + X41, X31 >= 0, X41 >= 0, X13 >= 0, X23 >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U22(mark(X12), X22, X3'', X4'')) :|: z = 2, X12 >= 0, X22 >= 0, X3'' >= 0, z' = 1 + X12 + X22 + X3'' + X4'', X4'' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U21(mark(X11), X21, X3', X4')) :|: z = 2, X3' >= 0, X4' >= 0, X11 >= 0, X21 >= 0, z' = 1 + X11 + X21 + X3' + X4' a__U12(z, z') -{ 2 }-> 1 + a__length(a__U12(mark(X1''), X2'')) :|: z = 2, z' = 1 + X1'' + X2'', X1'' >= 0, X2'' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U11(mark(X1'), X2')) :|: z = 2, z' = 1 + X1' + X2', X2' >= 0, X1' >= 0 a__U12(z, z') -{ 3 }-> 1 + a__length(3) :|: z = 2, z' = 3 a__U12(z, z') -{ 2 }-> 1 + a__length(2) :|: z = 2, z' = 2 a__U12(z, z') -{ 2 }-> 1 + a__length(1) :|: z = 2, z' = 1 a__U12(z, z') -{ 2 }-> 1 + a__length(0) :|: z = 2, z' = 0 a__U12(z, z') -{ 2 }-> 1 + a__length(1 + mark(X'')) :|: z = 2, z' = 1 + X'', X'' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(1 + mark(X15) + X25) :|: z = 2, z' = 1 + X15 + X25, X15 >= 0, X25 >= 0 a__U12(z, z') -{ 3 }-> 1 + a__length(1 + 0 + 3) :|: z = 2, z' = 3 a__U12(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U21(z, z', z'', z1) -{ 1 }-> a__U22(2, IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U21(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U22(z, z', z'', z1) -{ 1 }-> a__U23(2, IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U22(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U23(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U23(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__length(z) -{ 1 }-> a__U11(2, L) :|: z = 1 + N + L, L >= 0, N >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__take(z, z') -{ 1 }-> a__U21(2, IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, 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__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(X125), mark(X225))) :|: X125 >= 0, X225 >= 0, z = 1 + (1 + X125 + X225) mark(z) -{ 2 }-> a__length(a__length(mark(X9))) :|: X9 >= 0, z = 1 + (1 + X9) mark(z) -{ 2 }-> a__length(a__U23(mark(X124), X224, X310, X410)) :|: X124 >= 0, X410 >= 0, X224 >= 0, X310 >= 0, z = 1 + (1 + X124 + X224 + X310 + X410) mark(z) -{ 2 }-> a__length(a__U22(mark(X123), X223, X39, X49)) :|: X223 >= 0, z = 1 + (1 + X123 + X223 + X39 + X49), X49 >= 0, X39 >= 0, X123 >= 0 mark(z) -{ 2 }-> a__length(a__U21(mark(X122), X222, X38, X48)) :|: X222 >= 0, X48 >= 0, X38 >= 0, X122 >= 0, z = 1 + (1 + X122 + X222 + X38 + X48) mark(z) -{ 2 }-> a__length(a__U12(mark(X121), X221)) :|: z = 1 + (1 + X121 + X221), X221 >= 0, X121 >= 0 mark(z) -{ 2 }-> a__length(a__U11(mark(X120), X220)) :|: X120 >= 0, z = 1 + (1 + X120 + X220), X220 >= 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(X10)) :|: z = 1 + (1 + X10), X10 >= 0 mark(z) -{ 2 }-> a__length(1 + mark(X126) + X226) :|: z = 1 + (1 + X126 + X226), X126 >= 0, X226 >= 0 mark(z) -{ 3 }-> a__length(1 + 0 + 3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__U23(a__take(mark(X146), mark(X246)), X2, X3, X4) :|: X146 >= 0, z = 1 + (1 + X146 + X246) + X2 + X3 + X4, X246 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__length(mark(X51)), X2, X3, X4) :|: X51 >= 0, z = 1 + (1 + X51) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U23(mark(X145), X245, X319, X419), X2, X3, X4) :|: X319 >= 0, X245 >= 0, X145 >= 0, X419 >= 0, X3 >= 0, z = 1 + (1 + X145 + X245 + X319 + X419) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U22(mark(X144), X244, X318, X418), X2, X3, X4) :|: X244 >= 0, X418 >= 0, X144 >= 0, z = 1 + (1 + X144 + X244 + X318 + X418) + X2 + X3 + X4, X3 >= 0, X318 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U21(mark(X143), X243, X317, X417), X2, X3, X4) :|: X243 >= 0, X3 >= 0, X143 >= 0, X417 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X143 + X243 + X317 + X417) + X2 + X3 + X4, X317 >= 0 mark(z) -{ 2 }-> a__U23(a__U12(mark(X142), X242), X2, X3, X4) :|: X242 >= 0, X3 >= 0, z = 1 + (1 + X142 + X242) + X2 + X3 + X4, X2 >= 0, X4 >= 0, X142 >= 0 mark(z) -{ 2 }-> a__U23(a__U11(mark(X141), X241), X2, X3, X4) :|: z = 1 + (1 + X141 + X241) + X2 + X3 + X4, X3 >= 0, X241 >= 0, X2 >= 0, X4 >= 0, X141 >= 0 mark(z) -{ 3 }-> a__U23(3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U23(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U23(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(1 + mark(X52), X2, X3, X4) :|: X3 >= 0, z = 1 + (1 + X52) + X2 + X3 + X4, X52 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(1 + mark(X147) + X247, X2, X3, X4) :|: X147 >= 0, X3 >= 0, z = 1 + (1 + X147 + X247) + X2 + X3 + X4, X247 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 3 }-> a__U23(1 + 0 + 3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__take(mark(X139), mark(X239)), X2, X3, X4) :|: z = 1 + (1 + X139 + X239) + X2 + X3 + X4, X3 >= 0, X239 >= 0, X2 >= 0, X4 >= 0, X139 >= 0 mark(z) -{ 2 }-> a__U22(a__length(mark(X40)), X2, X3, X4) :|: z = 1 + (1 + X40) + X2 + X3 + X4, X40 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__U23(mark(X138), X238, X316, X416), X2, X3, X4) :|: z = 1 + (1 + X138 + X238 + X316 + X416) + X2 + X3 + X4, X3 >= 0, X416 >= 0, X2 >= 0, X4 >= 0, X138 >= 0, X238 >= 0, X316 >= 0 mark(z) -{ 2 }-> a__U22(a__U22(mark(X137), X237, X315, X415), X2, X3, X4) :|: X315 >= 0, z = 1 + (1 + X137 + X237 + X315 + X415) + X2 + X3 + X4, X3 >= 0, X137 >= 0, X2 >= 0, X4 >= 0, X237 >= 0, X415 >= 0 mark(z) -{ 2 }-> a__U22(a__U21(mark(X136), X236, X314, X414), X2, X3, X4) :|: X414 >= 0, X136 >= 0, X3 >= 0, X236 >= 0, X314 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X136 + X236 + X314 + X414) + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(a__U12(mark(X135), X235), X2, X3, X4) :|: X135 >= 0, X3 >= 0, X235 >= 0, z = 1 + (1 + X135 + X235) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__U11(mark(X134), X234), X2, X3, X4) :|: X134 >= 0, X234 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X134 + X234) + X2 + X3 + X4 mark(z) -{ 3 }-> a__U22(3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(1 + mark(X50), X2, X3, X4) :|: X50 >= 0, X3 >= 0, z = 1 + (1 + X50) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(1 + mark(X140) + X240, X2, X3, X4) :|: X240 >= 0, z = 1 + (1 + X140 + X240) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0, X140 >= 0 mark(z) -{ 3 }-> a__U22(1 + 0 + 3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__take(mark(X132), mark(X232)), X2, X3, X4) :|: z = 1 + (1 + X132 + X232) + X2 + X3 + X4, X3 >= 0, X232 >= 0, X2 >= 0, X4 >= 0, X132 >= 0 mark(z) -{ 2 }-> a__U21(a__length(mark(X20)), X2, X3, X4) :|: z = 1 + (1 + X20) + X2 + X3 + X4, X20 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U23(mark(X131), X231, X313, X413), X2, X3, X4) :|: X313 >= 0, X3 >= 0, X231 >= 0, X413 >= 0, z = 1 + (1 + X131 + X231 + X313 + X413) + X2 + X3 + X4, X2 >= 0, X4 >= 0, X131 >= 0 mark(z) -{ 2 }-> a__U21(a__U22(mark(X130), X230, X312, X412), X2, X3, X4) :|: z = 1 + (1 + X130 + X230 + X312 + X412) + X2 + X3 + X4, X312 >= 0, X412 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, X130 >= 0, X230 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X129), X229, X311, X411), X2, X3, X4) :|: z = 1 + (1 + X129 + X229 + X311 + X411) + X2 + X3 + X4, X311 >= 0, X411 >= 0, X229 >= 0, X3 >= 0, X129 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U12(mark(X128), X228), X2, X3, X4) :|: X128 >= 0, z = 1 + (1 + X128 + X228) + X2 + X3 + X4, X3 >= 0, X228 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U11(mark(X127), X227), X2, X3, X4) :|: X227 >= 0, X3 >= 0, X127 >= 0, z = 1 + (1 + X127 + X227) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 3 }-> a__U21(3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(1 + mark(X30), X2, X3, X4) :|: X30 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X30) + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(1 + mark(X133) + X233, X2, X3, X4) :|: X233 >= 0, X3 >= 0, z = 1 + (1 + X133 + X233) + X2 + X3 + X4, X133 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 3 }-> a__U21(1 + 0 + 3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U12(a__take(mark(X118), mark(X218)), X2) :|: X118 >= 0, z = 1 + (1 + X118 + X218) + X2, X2 >= 0, X218 >= 0 mark(z) -{ 2 }-> a__U12(a__length(mark(X7)), X2) :|: z = 1 + (1 + X7) + X2, X7 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U23(mark(X117), X217, X37, X47), X2) :|: X47 >= 0, X37 >= 0, X117 >= 0, X2 >= 0, z = 1 + (1 + X117 + X217 + X37 + X47) + X2, X217 >= 0 mark(z) -{ 2 }-> a__U12(a__U22(mark(X116), X216, X36, X46), X2) :|: X216 >= 0, X36 >= 0, z = 1 + (1 + X116 + X216 + X36 + X46) + X2, X116 >= 0, X46 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U21(mark(X115), X215, X35, X45), X2) :|: X115 >= 0, X35 >= 0, X45 >= 0, z = 1 + (1 + X115 + X215 + X35 + X45) + X2, X215 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(X114), X214), X2) :|: X114 >= 0, z = 1 + (1 + X114 + X214) + X2, X214 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X113), X213), X2) :|: X113 >= 0, X213 >= 0, z = 1 + (1 + X113 + X213) + X2, X2 >= 0 mark(z) -{ 3 }-> a__U12(3, X2) :|: X2 >= 0, z = 1 + 3 + X2 mark(z) -{ 2 }-> a__U12(2, X2) :|: z = 1 + 2 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X8), X2) :|: z = 1 + (1 + X8) + X2, X8 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X119) + X219, X2) :|: z = 1 + (1 + X119 + X219) + X2, X219 >= 0, X2 >= 0, X119 >= 0 mark(z) -{ 3 }-> a__U12(1 + 0 + 3, X2) :|: X2 >= 0, z = 1 + 3 + X2 mark(z) -{ 2 }-> a__U11(a__take(mark(X111), mark(X211)), X2) :|: z = 1 + (1 + X111 + X211) + X2, X211 >= 0, X2 >= 0, X111 >= 0 mark(z) -{ 2 }-> a__U11(a__length(mark(X5)), X2) :|: X5 >= 0, z = 1 + (1 + X5) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U23(mark(X110), X210, X34, X44), X2) :|: X110 >= 0, z = 1 + (1 + X110 + X210 + X34 + X44) + X2, X2 >= 0, X210 >= 0, X34 >= 0, X44 >= 0 mark(z) -{ 2 }-> a__U11(a__U22(mark(X19), X29, X33, X43), X2) :|: X33 >= 0, X43 >= 0, X29 >= 0, X19 >= 0, z = 1 + (1 + X19 + X29 + X33 + X43) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X18), X28, X32, X42), X2) :|: X32 >= 0, X18 >= 0, X28 >= 0, z = 1 + (1 + X18 + X28 + X32 + X42) + X2, X42 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X17), X27), X2) :|: X17 >= 0, X27 >= 0, z = 1 + (1 + X17 + X27) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X16), X26), X2) :|: X16 >= 0, X26 >= 0, z = 1 + (1 + X16 + X26) + X2, X2 >= 0 mark(z) -{ 3 }-> a__U11(3, X2) :|: X2 >= 0, z = 1 + 3 + X2 mark(z) -{ 2 }-> a__U11(2, X2) :|: z = 1 + 2 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X6), X2) :|: X6 >= 0, z = 1 + (1 + X6) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X112) + X212, X2) :|: X212 >= 0, z = 1 + (1 + X112 + X212) + X2, X112 >= 0, X2 >= 0 mark(z) -{ 3 }-> a__U11(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 ---------------------------------------- (255) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (256) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z') -{ 1 }-> a__U12(2, z') :|: z = 2, z' >= 0 a__U11(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__take(mark(X14), mark(X24))) :|: z = 2, z' = 1 + X14 + X24, X14 >= 0, X24 >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__length(mark(z' - 1))) :|: z = 2, z' - 1 >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U23(mark(X13), X23, X31, X41)) :|: z = 2, z' = 1 + X13 + X23 + X31 + X41, X31 >= 0, X41 >= 0, X13 >= 0, X23 >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U22(mark(X12), X22, X3'', X4'')) :|: z = 2, X12 >= 0, X22 >= 0, X3'' >= 0, z' = 1 + X12 + X22 + X3'' + X4'', X4'' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U21(mark(X11), X21, X3', X4')) :|: z = 2, X3' >= 0, X4' >= 0, X11 >= 0, X21 >= 0, z' = 1 + X11 + X21 + X3' + X4' a__U12(z, z') -{ 2 }-> 1 + a__length(a__U12(mark(X1''), X2'')) :|: z = 2, z' = 1 + X1'' + X2'', X1'' >= 0, X2'' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U11(mark(X1'), X2')) :|: z = 2, z' = 1 + X1' + X2', X2' >= 0, X1' >= 0 a__U12(z, z') -{ 3 }-> 1 + a__length(3) :|: z = 2, z' = 3 a__U12(z, z') -{ 2 }-> 1 + a__length(2) :|: z = 2, z' = 2 a__U12(z, z') -{ 2 }-> 1 + a__length(1) :|: z = 2, z' = 1 a__U12(z, z') -{ 2 }-> 1 + a__length(0) :|: z = 2, z' = 0 a__U12(z, z') -{ 2 }-> 1 + a__length(1 + mark(z' - 1)) :|: z = 2, z' - 1 >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(1 + mark(X15) + X25) :|: z = 2, z' = 1 + X15 + X25, X15 >= 0, X25 >= 0 a__U12(z, z') -{ 3 }-> 1 + a__length(1 + 0 + 3) :|: z = 2, z' = 3 a__U12(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U21(z, z', z'', z1) -{ 1 }-> a__U22(2, z', z'', z1) :|: z = 2, z'' >= 0, z' >= 0, z1 >= 0 a__U21(z, z', z'', z1) -{ 1 }-> 1 + z + z' + z'' + z1 :|: z >= 0, z'' >= 0, z' >= 0, z1 >= 0 a__U22(z, z', z'', z1) -{ 1 }-> a__U23(2, z', z'', z1) :|: z = 2, z'' >= 0, z' >= 0, z1 >= 0 a__U22(z, z', z'', z1) -{ 1 }-> 1 + z + z' + z'' + z1 :|: z >= 0, z'' >= 0, z' >= 0, z1 >= 0 a__U23(z, z', z'', z1) -{ 1 }-> 1 + mark(z1) + (1 + z'' + z') :|: z = 2, z'' >= 0, z' >= 0, z1 >= 0 a__U23(z, z', z'', z1) -{ 1 }-> 1 + z + z' + z'' + z1 :|: z >= 0, z'' >= 0, z' >= 0, z1 >= 0 a__length(z) -{ 1 }-> a__U11(2, L) :|: z = 1 + N + L, L >= 0, N >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + z :|: z >= 0 a__take(z, z') -{ 1 }-> a__U21(2, IL, z - 1, N) :|: z - 1 >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__take(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0 a__take(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 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(X125), mark(X225))) :|: X125 >= 0, X225 >= 0, z = 1 + (1 + X125 + X225) mark(z) -{ 2 }-> a__length(a__length(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__length(a__U23(mark(X124), X224, X310, X410)) :|: X124 >= 0, X410 >= 0, X224 >= 0, X310 >= 0, z = 1 + (1 + X124 + X224 + X310 + X410) mark(z) -{ 2 }-> a__length(a__U22(mark(X123), X223, X39, X49)) :|: X223 >= 0, z = 1 + (1 + X123 + X223 + X39 + X49), X49 >= 0, X39 >= 0, X123 >= 0 mark(z) -{ 2 }-> a__length(a__U21(mark(X122), X222, X38, X48)) :|: X222 >= 0, X48 >= 0, X38 >= 0, X122 >= 0, z = 1 + (1 + X122 + X222 + X38 + X48) mark(z) -{ 2 }-> a__length(a__U12(mark(X121), X221)) :|: z = 1 + (1 + X121 + X221), X221 >= 0, X121 >= 0 mark(z) -{ 2 }-> a__length(a__U11(mark(X120), X220)) :|: X120 >= 0, z = 1 + (1 + X120 + X220), X220 >= 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(X126) + X226) :|: z = 1 + (1 + X126 + X226), X126 >= 0, X226 >= 0 mark(z) -{ 3 }-> a__length(1 + 0 + 3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__U23(a__take(mark(X146), mark(X246)), X2, X3, X4) :|: X146 >= 0, z = 1 + (1 + X146 + X246) + X2 + X3 + X4, X246 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__length(mark(X51)), X2, X3, X4) :|: X51 >= 0, z = 1 + (1 + X51) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U23(mark(X145), X245, X319, X419), X2, X3, X4) :|: X319 >= 0, X245 >= 0, X145 >= 0, X419 >= 0, X3 >= 0, z = 1 + (1 + X145 + X245 + X319 + X419) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U22(mark(X144), X244, X318, X418), X2, X3, X4) :|: X244 >= 0, X418 >= 0, X144 >= 0, z = 1 + (1 + X144 + X244 + X318 + X418) + X2 + X3 + X4, X3 >= 0, X318 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U21(mark(X143), X243, X317, X417), X2, X3, X4) :|: X243 >= 0, X3 >= 0, X143 >= 0, X417 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X143 + X243 + X317 + X417) + X2 + X3 + X4, X317 >= 0 mark(z) -{ 2 }-> a__U23(a__U12(mark(X142), X242), X2, X3, X4) :|: X242 >= 0, X3 >= 0, z = 1 + (1 + X142 + X242) + X2 + X3 + X4, X2 >= 0, X4 >= 0, X142 >= 0 mark(z) -{ 2 }-> a__U23(a__U11(mark(X141), X241), X2, X3, X4) :|: z = 1 + (1 + X141 + X241) + X2 + X3 + X4, X3 >= 0, X241 >= 0, X2 >= 0, X4 >= 0, X141 >= 0 mark(z) -{ 3 }-> a__U23(3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U23(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U23(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(1 + mark(X52), X2, X3, X4) :|: X3 >= 0, z = 1 + (1 + X52) + X2 + X3 + X4, X52 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(1 + mark(X147) + X247, X2, X3, X4) :|: X147 >= 0, X3 >= 0, z = 1 + (1 + X147 + X247) + X2 + X3 + X4, X247 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 3 }-> a__U23(1 + 0 + 3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__take(mark(X139), mark(X239)), X2, X3, X4) :|: z = 1 + (1 + X139 + X239) + X2 + X3 + X4, X3 >= 0, X239 >= 0, X2 >= 0, X4 >= 0, X139 >= 0 mark(z) -{ 2 }-> a__U22(a__length(mark(X40)), X2, X3, X4) :|: z = 1 + (1 + X40) + X2 + X3 + X4, X40 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__U23(mark(X138), X238, X316, X416), X2, X3, X4) :|: z = 1 + (1 + X138 + X238 + X316 + X416) + X2 + X3 + X4, X3 >= 0, X416 >= 0, X2 >= 0, X4 >= 0, X138 >= 0, X238 >= 0, X316 >= 0 mark(z) -{ 2 }-> a__U22(a__U22(mark(X137), X237, X315, X415), X2, X3, X4) :|: X315 >= 0, z = 1 + (1 + X137 + X237 + X315 + X415) + X2 + X3 + X4, X3 >= 0, X137 >= 0, X2 >= 0, X4 >= 0, X237 >= 0, X415 >= 0 mark(z) -{ 2 }-> a__U22(a__U21(mark(X136), X236, X314, X414), X2, X3, X4) :|: X414 >= 0, X136 >= 0, X3 >= 0, X236 >= 0, X314 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X136 + X236 + X314 + X414) + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(a__U12(mark(X135), X235), X2, X3, X4) :|: X135 >= 0, X3 >= 0, X235 >= 0, z = 1 + (1 + X135 + X235) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__U11(mark(X134), X234), X2, X3, X4) :|: X134 >= 0, X234 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X134 + X234) + X2 + X3 + X4 mark(z) -{ 3 }-> a__U22(3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(1 + mark(X50), X2, X3, X4) :|: X50 >= 0, X3 >= 0, z = 1 + (1 + X50) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(1 + mark(X140) + X240, X2, X3, X4) :|: X240 >= 0, z = 1 + (1 + X140 + X240) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0, X140 >= 0 mark(z) -{ 3 }-> a__U22(1 + 0 + 3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__take(mark(X132), mark(X232)), X2, X3, X4) :|: z = 1 + (1 + X132 + X232) + X2 + X3 + X4, X3 >= 0, X232 >= 0, X2 >= 0, X4 >= 0, X132 >= 0 mark(z) -{ 2 }-> a__U21(a__length(mark(X20)), X2, X3, X4) :|: z = 1 + (1 + X20) + X2 + X3 + X4, X20 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U23(mark(X131), X231, X313, X413), X2, X3, X4) :|: X313 >= 0, X3 >= 0, X231 >= 0, X413 >= 0, z = 1 + (1 + X131 + X231 + X313 + X413) + X2 + X3 + X4, X2 >= 0, X4 >= 0, X131 >= 0 mark(z) -{ 2 }-> a__U21(a__U22(mark(X130), X230, X312, X412), X2, X3, X4) :|: z = 1 + (1 + X130 + X230 + X312 + X412) + X2 + X3 + X4, X312 >= 0, X412 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, X130 >= 0, X230 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X129), X229, X311, X411), X2, X3, X4) :|: z = 1 + (1 + X129 + X229 + X311 + X411) + X2 + X3 + X4, X311 >= 0, X411 >= 0, X229 >= 0, X3 >= 0, X129 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U12(mark(X128), X228), X2, X3, X4) :|: X128 >= 0, z = 1 + (1 + X128 + X228) + X2 + X3 + X4, X3 >= 0, X228 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U11(mark(X127), X227), X2, X3, X4) :|: X227 >= 0, X3 >= 0, X127 >= 0, z = 1 + (1 + X127 + X227) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 3 }-> a__U21(3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(1 + mark(X30), X2, X3, X4) :|: X30 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X30) + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(1 + mark(X133) + X233, X2, X3, X4) :|: X233 >= 0, X3 >= 0, z = 1 + (1 + X133 + X233) + X2 + X3 + X4, X133 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 3 }-> a__U21(1 + 0 + 3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U12(a__take(mark(X118), mark(X218)), X2) :|: X118 >= 0, z = 1 + (1 + X118 + X218) + X2, X2 >= 0, X218 >= 0 mark(z) -{ 2 }-> a__U12(a__length(mark(X7)), X2) :|: z = 1 + (1 + X7) + X2, X7 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U23(mark(X117), X217, X37, X47), X2) :|: X47 >= 0, X37 >= 0, X117 >= 0, X2 >= 0, z = 1 + (1 + X117 + X217 + X37 + X47) + X2, X217 >= 0 mark(z) -{ 2 }-> a__U12(a__U22(mark(X116), X216, X36, X46), X2) :|: X216 >= 0, X36 >= 0, z = 1 + (1 + X116 + X216 + X36 + X46) + X2, X116 >= 0, X46 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U21(mark(X115), X215, X35, X45), X2) :|: X115 >= 0, X35 >= 0, X45 >= 0, z = 1 + (1 + X115 + X215 + X35 + X45) + X2, X215 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(X114), X214), X2) :|: X114 >= 0, z = 1 + (1 + X114 + X214) + X2, X214 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X113), X213), X2) :|: X113 >= 0, X213 >= 0, z = 1 + (1 + X113 + X213) + X2, X2 >= 0 mark(z) -{ 3 }-> a__U12(3, z - 4) :|: z - 4 >= 0 mark(z) -{ 2 }-> a__U12(2, z - 3) :|: z - 3 >= 0 mark(z) -{ 2 }-> a__U12(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U12(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X8), X2) :|: z = 1 + (1 + X8) + X2, X8 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X119) + X219, X2) :|: z = 1 + (1 + X119 + X219) + X2, X219 >= 0, X2 >= 0, X119 >= 0 mark(z) -{ 3 }-> a__U12(1 + 0 + 3, z - 4) :|: z - 4 >= 0 mark(z) -{ 2 }-> a__U11(a__take(mark(X111), mark(X211)), X2) :|: z = 1 + (1 + X111 + X211) + X2, X211 >= 0, X2 >= 0, X111 >= 0 mark(z) -{ 2 }-> a__U11(a__length(mark(X5)), X2) :|: X5 >= 0, z = 1 + (1 + X5) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U23(mark(X110), X210, X34, X44), X2) :|: X110 >= 0, z = 1 + (1 + X110 + X210 + X34 + X44) + X2, X2 >= 0, X210 >= 0, X34 >= 0, X44 >= 0 mark(z) -{ 2 }-> a__U11(a__U22(mark(X19), X29, X33, X43), X2) :|: X33 >= 0, X43 >= 0, X29 >= 0, X19 >= 0, z = 1 + (1 + X19 + X29 + X33 + X43) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X18), X28, X32, X42), X2) :|: X32 >= 0, X18 >= 0, X28 >= 0, z = 1 + (1 + X18 + X28 + X32 + X42) + X2, X42 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X17), X27), X2) :|: X17 >= 0, X27 >= 0, z = 1 + (1 + X17 + X27) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X16), X26), X2) :|: X16 >= 0, X26 >= 0, z = 1 + (1 + X16 + X26) + X2, X2 >= 0 mark(z) -{ 3 }-> a__U11(3, z - 4) :|: z - 4 >= 0 mark(z) -{ 2 }-> a__U11(2, z - 3) :|: z - 3 >= 0 mark(z) -{ 2 }-> a__U11(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U11(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X6), X2) :|: X6 >= 0, z = 1 + (1 + X6) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X112) + X212, X2) :|: X212 >= 0, z = 1 + (1 + X112 + X212) + X2, X112 >= 0, X2 >= 0 mark(z) -{ 3 }-> a__U11(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