KILLED proof of input_YvBUR9fcqc.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxRelTRS (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 8 ms] (12) typed CpxTrs (13) OrderProof [LOWER BOUND(ID), 0 ms] (14) typed CpxTrs (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 5 ms] (16) TRS for Loop Detection (17) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (18) CdtProblem (19) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CdtProblem (21) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CdtProblem (23) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CpxRelTRS (25) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (26) CpxTRS (27) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CpxWeightedTrs (29) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxTypedWeightedTrs (31) CompletionProof [UPPER BOUND(ID), 0 ms] (32) CpxTypedWeightedCompleteTrs (33) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CpxTypedWeightedCompleteTrs (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (36) CpxRNTS (37) InliningProof [UPPER BOUND(ID), 1717 ms] (38) CpxRNTS (39) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CpxRNTS (41) CompletionProof [UPPER BOUND(ID), 0 ms] (42) CpxTypedWeightedCompleteTrs (43) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtNarrowingProof [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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms] (74) CdtProblem (75) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 76 ms] (106) CdtProblem (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 87 ms] (110) CdtProblem (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 123 ms] (114) CdtProblem (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 81 ms] (118) CdtProblem (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 176 ms] (122) CdtProblem (123) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 185 ms] (126) CdtProblem (127) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 236 ms] (130) CdtProblem (131) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 263 ms] (134) CdtProblem (135) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtRewritingProof [BOTH BOUNDS(ID, ID), 25 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtRewritingProof [BOTH BOUNDS(ID, ID), 56 ms] (160) CdtProblem (161) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 44 ms] (164) CdtProblem (165) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtRewritingProof [BOTH BOUNDS(ID, ID), 33 ms] (170) CdtProblem (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtRewritingProof [BOTH BOUNDS(ID, ID), 11 ms] (174) CdtProblem (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms] (176) CdtProblem (177) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem (179) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 5 ms] (180) CdtProblem (181) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtRewritingProof [BOTH BOUNDS(ID, ID), 75 ms] (184) CdtProblem (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (186) CdtProblem (187) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 125 ms] (188) CdtProblem (189) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 6 ms] (190) CdtProblem (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (192) CdtProblem (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1220 ms] (194) CdtProblem (195) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (196) CdtProblem (197) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 19 ms] (198) CdtProblem (199) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (200) CdtProblem (201) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 39 ms] (202) CdtProblem (203) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 67 ms] (204) CdtProblem (205) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (206) CdtProblem (207) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 119 ms] (208) CdtProblem (209) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 164 ms] (210) CdtProblem (211) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (212) CdtProblem (213) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 1717 ms] (214) CdtProblem (215) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (216) CpxWeightedTrs (217) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (218) CpxTypedWeightedTrs (219) CompletionProof [UPPER BOUND(ID), 0 ms] (220) CpxTypedWeightedCompleteTrs (221) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (222) CpxTypedWeightedCompleteTrs (223) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (224) CpxRNTS (225) InliningProof [UPPER BOUND(ID), 908 ms] (226) CpxRNTS (227) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (228) CpxRNTS (229) CompletionProof [UPPER BOUND(ID), 0 ms] (230) CpxTypedWeightedCompleteTrs (231) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (232) 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__nats -> a__adx(a__zeros) a__zeros -> cons(0, zeros) a__incr(cons(X, Y)) -> cons(s(X), incr(Y)) a__adx(cons(X, Y)) -> a__incr(cons(X, adx(Y))) a__hd(cons(X, Y)) -> mark(X) a__tl(cons(X, Y)) -> mark(Y) mark(nats) -> a__nats mark(adx(X)) -> a__adx(mark(X)) mark(zeros) -> a__zeros mark(incr(X)) -> a__incr(mark(X)) mark(hd(X)) -> a__hd(mark(X)) mark(tl(X)) -> a__tl(mark(X)) mark(cons(X1, X2)) -> cons(X1, X2) mark(0) -> 0 mark(s(X)) -> s(X) a__nats -> nats a__adx(X) -> adx(X) a__zeros -> zeros a__incr(X) -> incr(X) a__hd(X) -> hd(X) a__tl(X) -> tl(X) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__nats -> a__adx(a__zeros) a__zeros -> cons(0', zeros) a__incr(cons(X, Y)) -> cons(s(X), incr(Y)) a__adx(cons(X, Y)) -> a__incr(cons(X, adx(Y))) a__hd(cons(X, Y)) -> mark(X) a__tl(cons(X, Y)) -> mark(Y) mark(nats) -> a__nats mark(adx(X)) -> a__adx(mark(X)) mark(zeros) -> a__zeros mark(incr(X)) -> a__incr(mark(X)) mark(hd(X)) -> a__hd(mark(X)) mark(tl(X)) -> a__tl(mark(X)) mark(cons(X1, X2)) -> cons(X1, X2) mark(0') -> 0' mark(s(X)) -> s(X) a__nats -> nats a__adx(X) -> adx(X) a__zeros -> zeros a__incr(X) -> incr(X) a__hd(X) -> hd(X) a__tl(X) -> tl(X) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__nats -> a__adx(a__zeros) a__zeros -> cons(0, zeros) a__incr(cons(X, Y)) -> cons(s(X), incr(Y)) a__adx(cons(X, Y)) -> a__incr(cons(X, adx(Y))) a__hd(cons(X, Y)) -> mark(X) a__tl(cons(X, Y)) -> mark(Y) mark(nats) -> a__nats mark(adx(X)) -> a__adx(mark(X)) mark(zeros) -> a__zeros mark(incr(X)) -> a__incr(mark(X)) mark(hd(X)) -> a__hd(mark(X)) mark(tl(X)) -> a__tl(mark(X)) mark(cons(X1, X2)) -> cons(X1, X2) mark(0) -> 0 mark(s(X)) -> s(X) a__nats -> nats a__adx(X) -> adx(X) a__zeros -> zeros a__incr(X) -> incr(X) a__hd(X) -> hd(X) a__tl(X) -> tl(X) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__NATS -> c(A__ADX(a__zeros), A__ZEROS) A__NATS -> c1 A__ZEROS -> c2 A__ZEROS -> c3 A__INCR(cons(z0, z1)) -> c4 A__INCR(z0) -> c5 A__ADX(cons(z0, z1)) -> c6(A__INCR(cons(z0, adx(z1)))) A__ADX(z0) -> c7 A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__HD(z0) -> c9 A__TL(cons(z0, z1)) -> c10(MARK(z1)) A__TL(z0) -> c11 MARK(nats) -> c12(A__NATS) MARK(adx(z0)) -> c13(A__ADX(mark(z0)), MARK(z0)) MARK(zeros) -> c14(A__ZEROS) MARK(incr(z0)) -> c15(A__INCR(mark(z0)), MARK(z0)) MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c18 MARK(0) -> c19 MARK(s(z0)) -> c20 S tuples: A__NATS -> c(A__ADX(a__zeros), A__ZEROS) A__NATS -> c1 A__ZEROS -> c2 A__ZEROS -> c3 A__INCR(cons(z0, z1)) -> c4 A__INCR(z0) -> c5 A__ADX(cons(z0, z1)) -> c6(A__INCR(cons(z0, adx(z1)))) A__ADX(z0) -> c7 A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__HD(z0) -> c9 A__TL(cons(z0, z1)) -> c10(MARK(z1)) A__TL(z0) -> c11 MARK(nats) -> c12(A__NATS) MARK(adx(z0)) -> c13(A__ADX(mark(z0)), MARK(z0)) MARK(zeros) -> c14(A__ZEROS) MARK(incr(z0)) -> c15(A__INCR(mark(z0)), MARK(z0)) MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c18 MARK(0) -> c19 MARK(s(z0)) -> c20 K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__NATS, A__ZEROS, A__INCR_1, A__ADX_1, A__HD_1, A__TL_1, MARK_1 Compound Symbols: c_2, c1, c2, c3, c4, c5, c6_1, c7, c8_1, c9, c10_1, c11, c12_1, c13_2, c14_1, c15_2, c16_2, c17_2, c18, c19, c20 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__NATS -> c(A__ADX(a__zeros), A__ZEROS) A__NATS -> c1 A__ZEROS -> c2 A__ZEROS -> c3 A__INCR(cons(z0, z1)) -> c4 A__INCR(z0) -> c5 A__ADX(cons(z0, z1)) -> c6(A__INCR(cons(z0, adx(z1)))) A__ADX(z0) -> c7 A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__HD(z0) -> c9 A__TL(cons(z0, z1)) -> c10(MARK(z1)) A__TL(z0) -> c11 MARK(nats) -> c12(A__NATS) MARK(adx(z0)) -> c13(A__ADX(mark(z0)), MARK(z0)) MARK(zeros) -> c14(A__ZEROS) MARK(incr(z0)) -> c15(A__INCR(mark(z0)), MARK(z0)) MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c18 MARK(0) -> c19 MARK(s(z0)) -> c20 The (relative) TRS S consists of the following rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Rewrite Strategy: INNERMOST ---------------------------------------- (9) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (10) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__NATS -> c(A__ADX(a__zeros), A__ZEROS) A__NATS -> c1 A__ZEROS -> c2 A__ZEROS -> c3 A__INCR(cons(z0, z1)) -> c4 A__INCR(z0) -> c5 A__ADX(cons(z0, z1)) -> c6(A__INCR(cons(z0, adx(z1)))) A__ADX(z0) -> c7 A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__HD(z0) -> c9 A__TL(cons(z0, z1)) -> c10(MARK(z1)) A__TL(z0) -> c11 MARK(nats) -> c12(A__NATS) MARK(adx(z0)) -> c13(A__ADX(mark(z0)), MARK(z0)) MARK(zeros) -> c14(A__ZEROS) MARK(incr(z0)) -> c15(A__INCR(mark(z0)), MARK(z0)) MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c18 MARK(0') -> c19 MARK(s(z0)) -> c20 The (relative) TRS S consists of the following rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0', zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0') -> 0' mark(s(z0)) -> s(z0) Rewrite Strategy: INNERMOST ---------------------------------------- (11) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (12) Obligation: Innermost TRS: Rules: A__NATS -> c(A__ADX(a__zeros), A__ZEROS) A__NATS -> c1 A__ZEROS -> c2 A__ZEROS -> c3 A__INCR(cons(z0, z1)) -> c4 A__INCR(z0) -> c5 A__ADX(cons(z0, z1)) -> c6(A__INCR(cons(z0, adx(z1)))) A__ADX(z0) -> c7 A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__HD(z0) -> c9 A__TL(cons(z0, z1)) -> c10(MARK(z1)) A__TL(z0) -> c11 MARK(nats) -> c12(A__NATS) MARK(adx(z0)) -> c13(A__ADX(mark(z0)), MARK(z0)) MARK(zeros) -> c14(A__ZEROS) MARK(incr(z0)) -> c15(A__INCR(mark(z0)), MARK(z0)) MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c18 MARK(0') -> c19 MARK(s(z0)) -> c20 a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0', zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0') -> 0' mark(s(z0)) -> s(z0) Types: A__NATS :: c:c1 c :: c6:c7 -> c2:c3 -> c:c1 A__ADX :: cons:adx:nats:zeros:incr:hd:tl:0':s -> c6:c7 a__zeros :: cons:adx:nats:zeros:incr:hd:tl:0':s A__ZEROS :: c2:c3 c1 :: c:c1 c2 :: c2:c3 c3 :: c2:c3 A__INCR :: cons:adx:nats:zeros:incr:hd:tl:0':s -> c4:c5 cons :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s c4 :: c4:c5 c5 :: c4:c5 c6 :: c4:c5 -> c6:c7 adx :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s c7 :: c6:c7 A__HD :: cons:adx:nats:zeros:incr:hd:tl:0':s -> c8:c9 c8 :: c12:c13:c14:c15:c16:c17:c18:c19:c20 -> c8:c9 MARK :: cons:adx:nats:zeros:incr:hd:tl:0':s -> c12:c13:c14:c15:c16:c17:c18:c19:c20 c9 :: c8:c9 A__TL :: cons:adx:nats:zeros:incr:hd:tl:0':s -> c10:c11 c10 :: c12:c13:c14:c15:c16:c17:c18:c19:c20 -> c10:c11 c11 :: c10:c11 nats :: cons:adx:nats:zeros:incr:hd:tl:0':s c12 :: c:c1 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 c13 :: c6:c7 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 mark :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s zeros :: cons:adx:nats:zeros:incr:hd:tl:0':s c14 :: c2:c3 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 incr :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s c15 :: c4:c5 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 hd :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s c16 :: c8:c9 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 tl :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s c17 :: c10:c11 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 c18 :: c12:c13:c14:c15:c16:c17:c18:c19:c20 0' :: cons:adx:nats:zeros:incr:hd:tl:0':s c19 :: c12:c13:c14:c15:c16:c17:c18:c19:c20 s :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s c20 :: c12:c13:c14:c15:c16:c17:c18:c19:c20 a__nats :: cons:adx:nats:zeros:incr:hd:tl:0':s a__adx :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s a__incr :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s a__hd :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s a__tl :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s hole_c:c11_21 :: c:c1 hole_c6:c72_21 :: c6:c7 hole_c2:c33_21 :: c2:c3 hole_cons:adx:nats:zeros:incr:hd:tl:0':s4_21 :: cons:adx:nats:zeros:incr:hd:tl:0':s hole_c4:c55_21 :: c4:c5 hole_c8:c96_21 :: c8:c9 hole_c12:c13:c14:c15:c16:c17:c18:c19:c207_21 :: c12:c13:c14:c15:c16:c17:c18:c19:c20 hole_c10:c118_21 :: c10:c11 gen_cons:adx:nats:zeros:incr:hd:tl:0':s9_21 :: Nat -> cons:adx:nats:zeros:incr:hd:tl:0':s gen_c12:c13:c14:c15:c16:c17:c18:c19:c2010_21 :: Nat -> c12:c13:c14:c15:c16:c17:c18:c19:c20 ---------------------------------------- (13) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: A__HD, MARK, A__TL, mark, a__hd, a__tl They will be analysed ascendingly in the following order: A__HD = MARK A__HD = A__TL MARK = A__TL mark < MARK mark = a__hd mark = a__tl a__hd = a__tl ---------------------------------------- (14) Obligation: Innermost TRS: Rules: A__NATS -> c(A__ADX(a__zeros), A__ZEROS) A__NATS -> c1 A__ZEROS -> c2 A__ZEROS -> c3 A__INCR(cons(z0, z1)) -> c4 A__INCR(z0) -> c5 A__ADX(cons(z0, z1)) -> c6(A__INCR(cons(z0, adx(z1)))) A__ADX(z0) -> c7 A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__HD(z0) -> c9 A__TL(cons(z0, z1)) -> c10(MARK(z1)) A__TL(z0) -> c11 MARK(nats) -> c12(A__NATS) MARK(adx(z0)) -> c13(A__ADX(mark(z0)), MARK(z0)) MARK(zeros) -> c14(A__ZEROS) MARK(incr(z0)) -> c15(A__INCR(mark(z0)), MARK(z0)) MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c18 MARK(0') -> c19 MARK(s(z0)) -> c20 a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0', zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0') -> 0' mark(s(z0)) -> s(z0) Types: A__NATS :: c:c1 c :: c6:c7 -> c2:c3 -> c:c1 A__ADX :: cons:adx:nats:zeros:incr:hd:tl:0':s -> c6:c7 a__zeros :: cons:adx:nats:zeros:incr:hd:tl:0':s A__ZEROS :: c2:c3 c1 :: c:c1 c2 :: c2:c3 c3 :: c2:c3 A__INCR :: cons:adx:nats:zeros:incr:hd:tl:0':s -> c4:c5 cons :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s c4 :: c4:c5 c5 :: c4:c5 c6 :: c4:c5 -> c6:c7 adx :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s c7 :: c6:c7 A__HD :: cons:adx:nats:zeros:incr:hd:tl:0':s -> c8:c9 c8 :: c12:c13:c14:c15:c16:c17:c18:c19:c20 -> c8:c9 MARK :: cons:adx:nats:zeros:incr:hd:tl:0':s -> c12:c13:c14:c15:c16:c17:c18:c19:c20 c9 :: c8:c9 A__TL :: cons:adx:nats:zeros:incr:hd:tl:0':s -> c10:c11 c10 :: c12:c13:c14:c15:c16:c17:c18:c19:c20 -> c10:c11 c11 :: c10:c11 nats :: cons:adx:nats:zeros:incr:hd:tl:0':s c12 :: c:c1 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 c13 :: c6:c7 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 mark :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s zeros :: cons:adx:nats:zeros:incr:hd:tl:0':s c14 :: c2:c3 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 incr :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s c15 :: c4:c5 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 hd :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s c16 :: c8:c9 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 tl :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s c17 :: c10:c11 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 -> c12:c13:c14:c15:c16:c17:c18:c19:c20 c18 :: c12:c13:c14:c15:c16:c17:c18:c19:c20 0' :: cons:adx:nats:zeros:incr:hd:tl:0':s c19 :: c12:c13:c14:c15:c16:c17:c18:c19:c20 s :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s c20 :: c12:c13:c14:c15:c16:c17:c18:c19:c20 a__nats :: cons:adx:nats:zeros:incr:hd:tl:0':s a__adx :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s a__incr :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s a__hd :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s a__tl :: cons:adx:nats:zeros:incr:hd:tl:0':s -> cons:adx:nats:zeros:incr:hd:tl:0':s hole_c:c11_21 :: c:c1 hole_c6:c72_21 :: c6:c7 hole_c2:c33_21 :: c2:c3 hole_cons:adx:nats:zeros:incr:hd:tl:0':s4_21 :: cons:adx:nats:zeros:incr:hd:tl:0':s hole_c4:c55_21 :: c4:c5 hole_c8:c96_21 :: c8:c9 hole_c12:c13:c14:c15:c16:c17:c18:c19:c207_21 :: c12:c13:c14:c15:c16:c17:c18:c19:c20 hole_c10:c118_21 :: c10:c11 gen_cons:adx:nats:zeros:incr:hd:tl:0':s9_21 :: Nat -> cons:adx:nats:zeros:incr:hd:tl:0':s gen_c12:c13:c14:c15:c16:c17:c18:c19:c2010_21 :: Nat -> c12:c13:c14:c15:c16:c17:c18:c19:c20 Generator Equations: gen_cons:adx:nats:zeros:incr:hd:tl:0':s9_21(0) <=> nats gen_cons:adx:nats:zeros:incr:hd:tl:0':s9_21(+(x, 1)) <=> cons(nats, gen_cons:adx:nats:zeros:incr:hd:tl:0':s9_21(x)) gen_c12:c13:c14:c15:c16:c17:c18:c19:c2010_21(0) <=> c12(c(c6(c4), c2)) gen_c12:c13:c14:c15:c16:c17:c18:c19:c2010_21(+(x, 1)) <=> c13(c6(c4), gen_c12:c13:c14:c15:c16:c17:c18:c19:c2010_21(x)) The following defined symbols remain to be analysed: a__hd, A__HD, MARK, A__TL, mark, a__tl They will be analysed ascendingly in the following order: A__HD = MARK A__HD = A__TL MARK = A__TL mark < MARK mark = a__hd mark = a__tl a__hd = a__tl ---------------------------------------- (15) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (16) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__NATS -> c(A__ADX(a__zeros), A__ZEROS) A__NATS -> c1 A__ZEROS -> c2 A__ZEROS -> c3 A__INCR(cons(z0, z1)) -> c4 A__INCR(z0) -> c5 A__ADX(cons(z0, z1)) -> c6(A__INCR(cons(z0, adx(z1)))) A__ADX(z0) -> c7 A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__HD(z0) -> c9 A__TL(cons(z0, z1)) -> c10(MARK(z1)) A__TL(z0) -> c11 MARK(nats) -> c12(A__NATS) MARK(adx(z0)) -> c13(A__ADX(mark(z0)), MARK(z0)) MARK(zeros) -> c14(A__ZEROS) MARK(incr(z0)) -> c15(A__INCR(mark(z0)), MARK(z0)) MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c18 MARK(0) -> c19 MARK(s(z0)) -> c20 The (relative) TRS S consists of the following rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Rewrite Strategy: INNERMOST ---------------------------------------- (17) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (18) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__NATS -> c(A__ADX(a__zeros), A__ZEROS) A__NATS -> c1 A__ZEROS -> c2 A__ZEROS -> c3 A__INCR(cons(z0, z1)) -> c4 A__INCR(z0) -> c5 A__ADX(cons(z0, z1)) -> c6(A__INCR(cons(z0, adx(z1)))) A__ADX(z0) -> c7 A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__HD(z0) -> c9 A__TL(cons(z0, z1)) -> c10(MARK(z1)) A__TL(z0) -> c11 MARK(nats) -> c12(A__NATS) MARK(adx(z0)) -> c13(A__ADX(mark(z0)), MARK(z0)) MARK(zeros) -> c14(A__ZEROS) MARK(incr(z0)) -> c15(A__INCR(mark(z0)), MARK(z0)) MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c18 MARK(0) -> c19 MARK(s(z0)) -> c20 S tuples: A__NATS -> c(A__ADX(a__zeros), A__ZEROS) A__NATS -> c1 A__ZEROS -> c2 A__ZEROS -> c3 A__INCR(cons(z0, z1)) -> c4 A__INCR(z0) -> c5 A__ADX(cons(z0, z1)) -> c6(A__INCR(cons(z0, adx(z1)))) A__ADX(z0) -> c7 A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__HD(z0) -> c9 A__TL(cons(z0, z1)) -> c10(MARK(z1)) A__TL(z0) -> c11 MARK(nats) -> c12(A__NATS) MARK(adx(z0)) -> c13(A__ADX(mark(z0)), MARK(z0)) MARK(zeros) -> c14(A__ZEROS) MARK(incr(z0)) -> c15(A__INCR(mark(z0)), MARK(z0)) MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c18 MARK(0) -> c19 MARK(s(z0)) -> c20 K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__NATS, A__ZEROS, A__INCR_1, A__ADX_1, A__HD_1, A__TL_1, MARK_1 Compound Symbols: c_2, c1, c2, c3, c4, c5, c6_1, c7, c8_1, c9, c10_1, c11, c12_1, c13_2, c14_1, c15_2, c16_2, c17_2, c18, c19, c20 ---------------------------------------- (19) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 15 trailing nodes: MARK(nats) -> c12(A__NATS) MARK(0) -> c19 A__ADX(cons(z0, z1)) -> c6(A__INCR(cons(z0, adx(z1)))) A__INCR(z0) -> c5 A__ZEROS -> c2 MARK(s(z0)) -> c20 A__ADX(z0) -> c7 A__NATS -> c1 A__INCR(cons(z0, z1)) -> c4 MARK(cons(z0, z1)) -> c18 MARK(zeros) -> c14(A__ZEROS) A__ZEROS -> c3 A__HD(z0) -> c9 A__NATS -> c(A__ADX(a__zeros), A__ZEROS) A__TL(z0) -> c11 ---------------------------------------- (20) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(A__ADX(mark(z0)), MARK(z0)) MARK(incr(z0)) -> c15(A__INCR(mark(z0)), MARK(z0)) MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(A__ADX(mark(z0)), MARK(z0)) MARK(incr(z0)) -> c15(A__INCR(mark(z0)), MARK(z0)) MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_2, c15_2, c16_2, c17_2 ---------------------------------------- (21) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (22) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c16_2, c17_2, c13_1, c15_1 ---------------------------------------- (23) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (24) 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__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) The (relative) TRS S consists of the following rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Rewrite Strategy: INNERMOST ---------------------------------------- (25) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (26) 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__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (27) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (28) 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__HD(cons(z0, z1)) -> c8(MARK(z0)) [1] A__TL(cons(z0, z1)) -> c10(MARK(z1)) [1] MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) [1] MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) [1] MARK(adx(z0)) -> c13(MARK(z0)) [1] MARK(incr(z0)) -> c15(MARK(z0)) [1] a__nats -> a__adx(a__zeros) [0] a__nats -> nats [0] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) [0] a__incr(z0) -> incr(z0) [0] a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) [0] a__adx(z0) -> adx(z0) [0] a__hd(cons(z0, z1)) -> mark(z0) [0] a__hd(z0) -> hd(z0) [0] a__tl(cons(z0, z1)) -> mark(z1) [0] a__tl(z0) -> tl(z0) [0] mark(nats) -> a__nats [0] mark(adx(z0)) -> a__adx(mark(z0)) [0] mark(zeros) -> a__zeros [0] mark(incr(z0)) -> a__incr(mark(z0)) [0] mark(hd(z0)) -> a__hd(mark(z0)) [0] mark(tl(z0)) -> a__tl(mark(z0)) [0] mark(cons(z0, z1)) -> cons(z0, z1) [0] mark(0) -> 0 [0] mark(s(z0)) -> s(z0) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (29) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (30) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__HD(cons(z0, z1)) -> c8(MARK(z0)) [1] A__TL(cons(z0, z1)) -> c10(MARK(z1)) [1] MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) [1] MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) [1] MARK(adx(z0)) -> c13(MARK(z0)) [1] MARK(incr(z0)) -> c15(MARK(z0)) [1] a__nats -> a__adx(a__zeros) [0] a__nats -> nats [0] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) [0] a__incr(z0) -> incr(z0) [0] a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) [0] a__adx(z0) -> adx(z0) [0] a__hd(cons(z0, z1)) -> mark(z0) [0] a__hd(z0) -> hd(z0) [0] a__tl(cons(z0, z1)) -> mark(z1) [0] a__tl(z0) -> tl(z0) [0] mark(nats) -> a__nats [0] mark(adx(z0)) -> a__adx(mark(z0)) [0] mark(zeros) -> a__zeros [0] mark(incr(z0)) -> a__incr(mark(z0)) [0] mark(hd(z0)) -> a__hd(mark(z0)) [0] mark(tl(z0)) -> a__tl(mark(z0)) [0] mark(cons(z0, z1)) -> cons(z0, z1) [0] mark(0) -> 0 [0] mark(s(z0)) -> s(z0) [0] The TRS has the following type information: A__HD :: cons:hd:tl:adx:incr:nats:0:zeros:s -> c8 cons :: cons:hd:tl:adx:incr:nats:0:zeros:s -> cons:hd:tl:adx:incr:nats:0:zeros:s -> cons:hd:tl:adx:incr:nats:0:zeros:s c8 :: c16:c17:c13:c15 -> c8 MARK :: cons:hd:tl:adx:incr:nats:0:zeros:s -> c16:c17:c13:c15 A__TL :: cons:hd:tl:adx:incr:nats:0:zeros:s -> c10 c10 :: c16:c17:c13:c15 -> c10 hd :: cons:hd:tl:adx:incr:nats:0:zeros:s -> cons:hd:tl:adx:incr:nats:0:zeros:s c16 :: c8 -> c16:c17:c13:c15 -> c16:c17:c13:c15 mark :: cons:hd:tl:adx:incr:nats:0:zeros:s -> cons:hd:tl:adx:incr:nats:0:zeros:s tl :: cons:hd:tl:adx:incr:nats:0:zeros:s -> cons:hd:tl:adx:incr:nats:0:zeros:s c17 :: c10 -> c16:c17:c13:c15 -> c16:c17:c13:c15 adx :: cons:hd:tl:adx:incr:nats:0:zeros:s -> cons:hd:tl:adx:incr:nats:0:zeros:s c13 :: c16:c17:c13:c15 -> c16:c17:c13:c15 incr :: cons:hd:tl:adx:incr:nats:0:zeros:s -> cons:hd:tl:adx:incr:nats:0:zeros:s c15 :: c16:c17:c13:c15 -> c16:c17:c13:c15 a__nats :: cons:hd:tl:adx:incr:nats:0:zeros:s a__adx :: cons:hd:tl:adx:incr:nats:0:zeros:s -> cons:hd:tl:adx:incr:nats:0:zeros:s a__zeros :: cons:hd:tl:adx:incr:nats:0:zeros:s nats :: cons:hd:tl:adx:incr:nats:0:zeros:s 0 :: cons:hd:tl:adx:incr:nats:0:zeros:s zeros :: cons:hd:tl:adx:incr:nats:0:zeros:s a__incr :: cons:hd:tl:adx:incr:nats:0:zeros:s -> cons:hd:tl:adx:incr:nats:0:zeros:s s :: cons:hd:tl:adx:incr:nats:0:zeros:s -> cons:hd:tl:adx:incr:nats:0:zeros:s a__hd :: cons:hd:tl:adx:incr:nats:0:zeros:s -> cons:hd:tl:adx:incr:nats:0:zeros:s a__tl :: cons:hd:tl:adx:incr:nats:0:zeros:s -> cons:hd:tl:adx:incr:nats:0:zeros:s Rewrite Strategy: INNERMOST ---------------------------------------- (31) 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__HD_1 A__TL_1 MARK_1 (c) The following functions are completely defined: a__nats a__zeros a__incr_1 a__adx_1 a__hd_1 a__tl_1 mark_1 Due to the following rules being added: a__nats -> null_a__nats [0] a__zeros -> null_a__zeros [0] a__incr(v0) -> null_a__incr [0] a__adx(v0) -> null_a__adx [0] a__hd(v0) -> null_a__hd [0] a__tl(v0) -> null_a__tl [0] mark(v0) -> null_mark [0] And the following fresh constants: null_a__nats, null_a__zeros, null_a__incr, null_a__adx, null_a__hd, null_a__tl, null_mark, const, const1, const2 ---------------------------------------- (32) 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__HD(cons(z0, z1)) -> c8(MARK(z0)) [1] A__TL(cons(z0, z1)) -> c10(MARK(z1)) [1] MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) [1] MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) [1] MARK(adx(z0)) -> c13(MARK(z0)) [1] MARK(incr(z0)) -> c15(MARK(z0)) [1] a__nats -> a__adx(a__zeros) [0] a__nats -> nats [0] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) [0] a__incr(z0) -> incr(z0) [0] a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) [0] a__adx(z0) -> adx(z0) [0] a__hd(cons(z0, z1)) -> mark(z0) [0] a__hd(z0) -> hd(z0) [0] a__tl(cons(z0, z1)) -> mark(z1) [0] a__tl(z0) -> tl(z0) [0] mark(nats) -> a__nats [0] mark(adx(z0)) -> a__adx(mark(z0)) [0] mark(zeros) -> a__zeros [0] mark(incr(z0)) -> a__incr(mark(z0)) [0] mark(hd(z0)) -> a__hd(mark(z0)) [0] mark(tl(z0)) -> a__tl(mark(z0)) [0] mark(cons(z0, z1)) -> cons(z0, z1) [0] mark(0) -> 0 [0] mark(s(z0)) -> s(z0) [0] a__nats -> null_a__nats [0] a__zeros -> null_a__zeros [0] a__incr(v0) -> null_a__incr [0] a__adx(v0) -> null_a__adx [0] a__hd(v0) -> null_a__hd [0] a__tl(v0) -> null_a__tl [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__HD :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> c8 cons :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark c8 :: c16:c17:c13:c15 -> c8 MARK :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> c16:c17:c13:c15 A__TL :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> c10 c10 :: c16:c17:c13:c15 -> c10 hd :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark c16 :: c8 -> c16:c17:c13:c15 -> c16:c17:c13:c15 mark :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark tl :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark c17 :: c10 -> c16:c17:c13:c15 -> c16:c17:c13:c15 adx :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark c13 :: c16:c17:c13:c15 -> c16:c17:c13:c15 incr :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark c15 :: c16:c17:c13:c15 -> c16:c17:c13:c15 a__nats :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark a__adx :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark a__zeros :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark nats :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark 0 :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark zeros :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark a__incr :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark s :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark a__hd :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark a__tl :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__nats :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__zeros :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__incr :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__adx :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__hd :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__tl :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_mark :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark const :: c8 const1 :: c16:c17:c13:c15 const2 :: c10 Rewrite Strategy: INNERMOST ---------------------------------------- (33) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (34) 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__HD(cons(z0, z1)) -> c8(MARK(z0)) [1] A__TL(cons(z0, z1)) -> c10(MARK(z1)) [1] MARK(hd(nats)) -> c16(A__HD(a__nats), MARK(nats)) [1] MARK(hd(adx(z0'))) -> c16(A__HD(a__adx(mark(z0'))), MARK(adx(z0'))) [1] MARK(hd(zeros)) -> c16(A__HD(a__zeros), MARK(zeros)) [1] MARK(hd(incr(z0''))) -> c16(A__HD(a__incr(mark(z0''))), MARK(incr(z0''))) [1] MARK(hd(hd(z01))) -> c16(A__HD(a__hd(mark(z01))), MARK(hd(z01))) [1] MARK(hd(tl(z02))) -> c16(A__HD(a__tl(mark(z02))), MARK(tl(z02))) [1] MARK(hd(cons(z03, z1'))) -> c16(A__HD(cons(z03, z1')), MARK(cons(z03, z1'))) [1] MARK(hd(0)) -> c16(A__HD(0), MARK(0)) [1] MARK(hd(s(z04))) -> c16(A__HD(s(z04)), MARK(s(z04))) [1] MARK(hd(z0)) -> c16(A__HD(null_mark), MARK(z0)) [1] MARK(tl(nats)) -> c17(A__TL(a__nats), MARK(nats)) [1] MARK(tl(adx(z05))) -> c17(A__TL(a__adx(mark(z05))), MARK(adx(z05))) [1] MARK(tl(zeros)) -> c17(A__TL(a__zeros), MARK(zeros)) [1] MARK(tl(incr(z06))) -> c17(A__TL(a__incr(mark(z06))), MARK(incr(z06))) [1] MARK(tl(hd(z07))) -> c17(A__TL(a__hd(mark(z07))), MARK(hd(z07))) [1] MARK(tl(tl(z08))) -> c17(A__TL(a__tl(mark(z08))), MARK(tl(z08))) [1] MARK(tl(cons(z09, z1''))) -> c17(A__TL(cons(z09, z1'')), MARK(cons(z09, z1''))) [1] MARK(tl(0)) -> c17(A__TL(0), MARK(0)) [1] MARK(tl(s(z010))) -> c17(A__TL(s(z010)), MARK(s(z010))) [1] MARK(tl(z0)) -> c17(A__TL(null_mark), MARK(z0)) [1] MARK(adx(z0)) -> c13(MARK(z0)) [1] MARK(incr(z0)) -> c15(MARK(z0)) [1] a__nats -> a__adx(cons(0, zeros)) [0] a__nats -> a__adx(zeros) [0] a__nats -> a__adx(null_a__zeros) [0] a__nats -> nats [0] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) [0] a__incr(z0) -> incr(z0) [0] a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) [0] a__adx(z0) -> adx(z0) [0] a__hd(cons(z0, z1)) -> mark(z0) [0] a__hd(z0) -> hd(z0) [0] a__tl(cons(z0, z1)) -> mark(z1) [0] a__tl(z0) -> tl(z0) [0] mark(nats) -> a__nats [0] mark(adx(nats)) -> a__adx(a__nats) [0] mark(adx(adx(z011))) -> a__adx(a__adx(mark(z011))) [0] mark(adx(zeros)) -> a__adx(a__zeros) [0] mark(adx(incr(z012))) -> a__adx(a__incr(mark(z012))) [0] mark(adx(hd(z013))) -> a__adx(a__hd(mark(z013))) [0] mark(adx(tl(z014))) -> a__adx(a__tl(mark(z014))) [0] mark(adx(cons(z015, z11))) -> a__adx(cons(z015, z11)) [0] mark(adx(0)) -> a__adx(0) [0] mark(adx(s(z016))) -> a__adx(s(z016)) [0] mark(adx(z0)) -> a__adx(null_mark) [0] mark(zeros) -> a__zeros [0] mark(incr(nats)) -> a__incr(a__nats) [0] mark(incr(adx(z017))) -> a__incr(a__adx(mark(z017))) [0] mark(incr(zeros)) -> a__incr(a__zeros) [0] mark(incr(incr(z018))) -> a__incr(a__incr(mark(z018))) [0] mark(incr(hd(z019))) -> a__incr(a__hd(mark(z019))) [0] mark(incr(tl(z020))) -> a__incr(a__tl(mark(z020))) [0] mark(incr(cons(z021, z12))) -> a__incr(cons(z021, z12)) [0] mark(incr(0)) -> a__incr(0) [0] mark(incr(s(z022))) -> a__incr(s(z022)) [0] mark(incr(z0)) -> a__incr(null_mark) [0] mark(hd(nats)) -> a__hd(a__nats) [0] mark(hd(adx(z023))) -> a__hd(a__adx(mark(z023))) [0] mark(hd(zeros)) -> a__hd(a__zeros) [0] mark(hd(incr(z024))) -> a__hd(a__incr(mark(z024))) [0] mark(hd(hd(z025))) -> a__hd(a__hd(mark(z025))) [0] mark(hd(tl(z026))) -> a__hd(a__tl(mark(z026))) [0] mark(hd(cons(z027, z13))) -> a__hd(cons(z027, z13)) [0] mark(hd(0)) -> a__hd(0) [0] mark(hd(s(z028))) -> a__hd(s(z028)) [0] mark(hd(z0)) -> a__hd(null_mark) [0] mark(tl(nats)) -> a__tl(a__nats) [0] mark(tl(adx(z029))) -> a__tl(a__adx(mark(z029))) [0] mark(tl(zeros)) -> a__tl(a__zeros) [0] mark(tl(incr(z030))) -> a__tl(a__incr(mark(z030))) [0] mark(tl(hd(z031))) -> a__tl(a__hd(mark(z031))) [0] mark(tl(tl(z032))) -> a__tl(a__tl(mark(z032))) [0] mark(tl(cons(z033, z14))) -> a__tl(cons(z033, z14)) [0] mark(tl(0)) -> a__tl(0) [0] mark(tl(s(z034))) -> a__tl(s(z034)) [0] mark(tl(z0)) -> a__tl(null_mark) [0] mark(cons(z0, z1)) -> cons(z0, z1) [0] mark(0) -> 0 [0] mark(s(z0)) -> s(z0) [0] a__nats -> null_a__nats [0] a__zeros -> null_a__zeros [0] a__incr(v0) -> null_a__incr [0] a__adx(v0) -> null_a__adx [0] a__hd(v0) -> null_a__hd [0] a__tl(v0) -> null_a__tl [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__HD :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> c8 cons :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark c8 :: c16:c17:c13:c15 -> c8 MARK :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> c16:c17:c13:c15 A__TL :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> c10 c10 :: c16:c17:c13:c15 -> c10 hd :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark c16 :: c8 -> c16:c17:c13:c15 -> c16:c17:c13:c15 mark :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark tl :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark c17 :: c10 -> c16:c17:c13:c15 -> c16:c17:c13:c15 adx :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark c13 :: c16:c17:c13:c15 -> c16:c17:c13:c15 incr :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark c15 :: c16:c17:c13:c15 -> c16:c17:c13:c15 a__nats :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark a__adx :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark a__zeros :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark nats :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark 0 :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark zeros :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark a__incr :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark s :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark a__hd :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark a__tl :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__nats :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__zeros :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__incr :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__adx :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__hd :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__tl :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_mark :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark const :: c8 const1 :: c16:c17:c13:c15 const2 :: c10 Rewrite Strategy: INNERMOST ---------------------------------------- (35) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: nats => 1 0 => 0 zeros => 2 null_a__nats => 0 null_a__zeros => 0 null_a__incr => 0 null_a__adx => 0 null_a__hd => 0 null_a__tl => 0 null_mark => 0 const => 0 const1 => 0 const2 => 0 ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: A__HD(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TL(z) -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__TL(a__zeros) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__TL(a__tl(mark(z08))) + MARK(1 + z08) :|: z08 >= 0, z = 1 + (1 + z08) MARK(z) -{ 1 }-> 1 + A__TL(a__nats) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__TL(a__incr(mark(z06))) + MARK(1 + z06) :|: z06 >= 0, z = 1 + (1 + z06) MARK(z) -{ 1 }-> 1 + A__TL(a__hd(mark(z07))) + MARK(1 + z07) :|: z = 1 + (1 + z07), z07 >= 0 MARK(z) -{ 1 }-> 1 + A__TL(a__adx(mark(z05))) + MARK(1 + z05) :|: z05 >= 0, z = 1 + (1 + z05) MARK(z) -{ 1 }-> 1 + A__TL(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__TL(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__TL(1 + z010) + MARK(1 + z010) :|: z = 1 + (1 + z010), z010 >= 0 MARK(z) -{ 1 }-> 1 + A__TL(1 + z09 + z1'') + MARK(1 + z09 + z1'') :|: z = 1 + (1 + z09 + z1''), z09 >= 0, z1'' >= 0 MARK(z) -{ 1 }-> 1 + A__HD(a__zeros) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__HD(a__tl(mark(z02))) + MARK(1 + z02) :|: z = 1 + (1 + z02), z02 >= 0 MARK(z) -{ 1 }-> 1 + A__HD(a__nats) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__HD(a__incr(mark(z0''))) + MARK(1 + z0'') :|: z = 1 + (1 + z0''), z0'' >= 0 MARK(z) -{ 1 }-> 1 + A__HD(a__hd(mark(z01))) + MARK(1 + z01) :|: z = 1 + (1 + z01), z01 >= 0 MARK(z) -{ 1 }-> 1 + A__HD(a__adx(mark(z0'))) + MARK(1 + z0') :|: z = 1 + (1 + z0'), z0' >= 0 MARK(z) -{ 1 }-> 1 + A__HD(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__HD(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__HD(1 + z04) + MARK(1 + z04) :|: z04 >= 0, z = 1 + (1 + z04) MARK(z) -{ 1 }-> 1 + A__HD(1 + z03 + z1') + MARK(1 + z03 + z1') :|: z1' >= 0, z03 >= 0, z = 1 + (1 + z03 + z1') a__adx(z) -{ 0 }-> a__incr(1 + z0 + (1 + z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__adx(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__adx(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__hd(z) -{ 0 }-> mark(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__hd(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__hd(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__incr(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__incr(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__incr(z) -{ 0 }-> 1 + (1 + z0) + (1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__nats -{ 0 }-> a__adx(2) :|: a__nats -{ 0 }-> a__adx(0) :|: a__nats -{ 0 }-> a__adx(1 + 0 + 2) :|: a__nats -{ 0 }-> 1 :|: a__nats -{ 0 }-> 0 :|: a__tl(z) -{ 0 }-> mark(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__tl(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__tl(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__zeros -{ 0 }-> 2 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 2 :|: mark(z) -{ 0 }-> a__zeros :|: z = 2 mark(z) -{ 0 }-> a__tl(a__zeros) :|: z = 1 + 2 mark(z) -{ 0 }-> a__tl(a__tl(mark(z032))) :|: z032 >= 0, z = 1 + (1 + z032) mark(z) -{ 0 }-> a__tl(a__nats) :|: z = 1 + 1 mark(z) -{ 0 }-> a__tl(a__incr(mark(z030))) :|: z = 1 + (1 + z030), z030 >= 0 mark(z) -{ 0 }-> a__tl(a__hd(mark(z031))) :|: z031 >= 0, z = 1 + (1 + z031) mark(z) -{ 0 }-> a__tl(a__adx(mark(z029))) :|: z029 >= 0, z = 1 + (1 + z029) mark(z) -{ 0 }-> a__tl(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__tl(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__tl(1 + z034) :|: z034 >= 0, z = 1 + (1 + z034) mark(z) -{ 0 }-> a__tl(1 + z033 + z14) :|: z = 1 + (1 + z033 + z14), z033 >= 0, z14 >= 0 mark(z) -{ 0 }-> a__nats :|: z = 1 mark(z) -{ 0 }-> a__incr(a__zeros) :|: z = 1 + 2 mark(z) -{ 0 }-> a__incr(a__tl(mark(z020))) :|: z = 1 + (1 + z020), z020 >= 0 mark(z) -{ 0 }-> a__incr(a__nats) :|: z = 1 + 1 mark(z) -{ 0 }-> a__incr(a__incr(mark(z018))) :|: z = 1 + (1 + z018), z018 >= 0 mark(z) -{ 0 }-> a__incr(a__hd(mark(z019))) :|: z019 >= 0, z = 1 + (1 + z019) mark(z) -{ 0 }-> a__incr(a__adx(mark(z017))) :|: z = 1 + (1 + z017), z017 >= 0 mark(z) -{ 0 }-> a__incr(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__incr(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__incr(1 + z022) :|: z022 >= 0, z = 1 + (1 + z022) mark(z) -{ 0 }-> a__incr(1 + z021 + z12) :|: z021 >= 0, z = 1 + (1 + z021 + z12), z12 >= 0 mark(z) -{ 0 }-> a__hd(a__zeros) :|: z = 1 + 2 mark(z) -{ 0 }-> a__hd(a__tl(mark(z026))) :|: z = 1 + (1 + z026), z026 >= 0 mark(z) -{ 0 }-> a__hd(a__nats) :|: z = 1 + 1 mark(z) -{ 0 }-> a__hd(a__incr(mark(z024))) :|: z024 >= 0, z = 1 + (1 + z024) mark(z) -{ 0 }-> a__hd(a__hd(mark(z025))) :|: z025 >= 0, z = 1 + (1 + z025) mark(z) -{ 0 }-> a__hd(a__adx(mark(z023))) :|: z023 >= 0, z = 1 + (1 + z023) mark(z) -{ 0 }-> a__hd(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__hd(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__hd(1 + z028) :|: z028 >= 0, z = 1 + (1 + z028) mark(z) -{ 0 }-> a__hd(1 + z027 + z13) :|: z027 >= 0, z = 1 + (1 + z027 + z13), z13 >= 0 mark(z) -{ 0 }-> a__adx(a__zeros) :|: z = 1 + 2 mark(z) -{ 0 }-> a__adx(a__tl(mark(z014))) :|: z = 1 + (1 + z014), z014 >= 0 mark(z) -{ 0 }-> a__adx(a__nats) :|: z = 1 + 1 mark(z) -{ 0 }-> a__adx(a__incr(mark(z012))) :|: z012 >= 0, z = 1 + (1 + z012) mark(z) -{ 0 }-> a__adx(a__hd(mark(z013))) :|: z013 >= 0, z = 1 + (1 + z013) mark(z) -{ 0 }-> a__adx(a__adx(mark(z011))) :|: z = 1 + (1 + z011), z011 >= 0 mark(z) -{ 0 }-> a__adx(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__adx(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__adx(1 + z016) :|: z016 >= 0, z = 1 + (1 + z016) mark(z) -{ 0 }-> a__adx(1 + z015 + z11) :|: z = 1 + (1 + z015 + z11), z015 >= 0, z11 >= 0 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ---------------------------------------- (37) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__zeros -{ 0 }-> 1 + 0 + 2 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 2 :|: a__incr(z) -{ 0 }-> 1 + (1 + z0) + (1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__incr(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__incr(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__adx(z) -{ 0 }-> a__incr(1 + z0 + (1 + z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__adx(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__adx(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 ---------------------------------------- (38) Obligation: Complexity RNTS consisting of the following rules: A__HD(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TL(z) -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__TL(a__tl(mark(z08))) + MARK(1 + z08) :|: z08 >= 0, z = 1 + (1 + z08) MARK(z) -{ 1 }-> 1 + A__TL(a__nats) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__TL(a__incr(mark(z06))) + MARK(1 + z06) :|: z06 >= 0, z = 1 + (1 + z06) MARK(z) -{ 1 }-> 1 + A__TL(a__hd(mark(z07))) + MARK(1 + z07) :|: z = 1 + (1 + z07), z07 >= 0 MARK(z) -{ 1 }-> 1 + A__TL(a__adx(mark(z05))) + MARK(1 + z05) :|: z05 >= 0, z = 1 + (1 + z05) MARK(z) -{ 1 }-> 1 + A__TL(2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__TL(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__TL(0) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__TL(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__TL(1 + z010) + MARK(1 + z010) :|: z = 1 + (1 + z010), z010 >= 0 MARK(z) -{ 1 }-> 1 + A__TL(1 + z09 + z1'') + MARK(1 + z09 + z1'') :|: z = 1 + (1 + z09 + z1''), z09 >= 0, z1'' >= 0 MARK(z) -{ 1 }-> 1 + A__TL(1 + 0 + 2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__HD(a__tl(mark(z02))) + MARK(1 + z02) :|: z = 1 + (1 + z02), z02 >= 0 MARK(z) -{ 1 }-> 1 + A__HD(a__nats) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__HD(a__incr(mark(z0''))) + MARK(1 + z0'') :|: z = 1 + (1 + z0''), z0'' >= 0 MARK(z) -{ 1 }-> 1 + A__HD(a__hd(mark(z01))) + MARK(1 + z01) :|: z = 1 + (1 + z01), z01 >= 0 MARK(z) -{ 1 }-> 1 + A__HD(a__adx(mark(z0'))) + MARK(1 + z0') :|: z = 1 + (1 + z0'), z0' >= 0 MARK(z) -{ 1 }-> 1 + A__HD(2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__HD(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__HD(0) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__HD(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__HD(1 + z04) + MARK(1 + z04) :|: z04 >= 0, z = 1 + (1 + z04) MARK(z) -{ 1 }-> 1 + A__HD(1 + z03 + z1') + MARK(1 + z03 + z1') :|: z1' >= 0, z03 >= 0, z = 1 + (1 + z03 + z1') MARK(z) -{ 1 }-> 1 + A__HD(1 + 0 + 2) + MARK(2) :|: z = 1 + 2 a__adx(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__adx(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, 1 + z0 + (1 + z1) = v0 a__adx(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__adx(z) -{ 0 }-> 1 + z0' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 1 + z0 + (1 + z1) = z0', z0' >= 0 a__adx(z) -{ 0 }-> 1 + (1 + z0') + (1 + z1') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + z0 + (1 + z1) = 1 + z0' + z1' a__hd(z) -{ 0 }-> mark(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__hd(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__hd(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__incr(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__incr(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__incr(z) -{ 0 }-> 1 + (1 + z0) + (1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__nats -{ 0 }-> a__incr(1 + z0 + (1 + z1)) :|: z1 >= 0, z0 >= 0, 1 + 0 + 2 = 1 + z0 + z1 a__nats -{ 0 }-> a__incr(1 + z0 + (1 + z1)) :|: z1 >= 0, z0 >= 0, 2 = 1 + z0 + z1 a__nats -{ 0 }-> 1 :|: a__nats -{ 0 }-> 0 :|: a__nats -{ 0 }-> 0 :|: v0 >= 0, 1 + 0 + 2 = v0 a__nats -{ 0 }-> 0 :|: v0 >= 0, 2 = v0 a__nats -{ 0 }-> 0 :|: v0 >= 0, 0 = v0 a__nats -{ 0 }-> 1 + z0 :|: 1 + 0 + 2 = z0, z0 >= 0 a__nats -{ 0 }-> 1 + z0 :|: 2 = z0, z0 >= 0 a__nats -{ 0 }-> 1 + z0 :|: 0 = z0, z0 >= 0 a__tl(z) -{ 0 }-> mark(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__tl(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__tl(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__zeros -{ 0 }-> 2 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 2 :|: mark(z) -{ 0 }-> a__tl(a__tl(mark(z032))) :|: z032 >= 0, z = 1 + (1 + z032) mark(z) -{ 0 }-> a__tl(a__nats) :|: z = 1 + 1 mark(z) -{ 0 }-> a__tl(a__incr(mark(z030))) :|: z = 1 + (1 + z030), z030 >= 0 mark(z) -{ 0 }-> a__tl(a__hd(mark(z031))) :|: z031 >= 0, z = 1 + (1 + z031) mark(z) -{ 0 }-> a__tl(a__adx(mark(z029))) :|: z029 >= 0, z = 1 + (1 + z029) mark(z) -{ 0 }-> a__tl(2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__tl(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__tl(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__tl(0) :|: z = 1 + 2 mark(z) -{ 0 }-> a__tl(1 + z034) :|: z034 >= 0, z = 1 + (1 + z034) mark(z) -{ 0 }-> a__tl(1 + z033 + z14) :|: z = 1 + (1 + z033 + z14), z033 >= 0, z14 >= 0 mark(z) -{ 0 }-> a__tl(1 + 0 + 2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__nats :|: z = 1 mark(z) -{ 0 }-> a__incr(a__tl(mark(z020))) :|: z = 1 + (1 + z020), z020 >= 0 mark(z) -{ 0 }-> a__incr(a__nats) :|: z = 1 + 1 mark(z) -{ 0 }-> a__incr(a__incr(mark(z018))) :|: z = 1 + (1 + z018), z018 >= 0 mark(z) -{ 0 }-> a__incr(a__hd(mark(z019))) :|: z019 >= 0, z = 1 + (1 + z019) mark(z) -{ 0 }-> a__incr(a__adx(mark(z017))) :|: z = 1 + (1 + z017), z017 >= 0 mark(z) -{ 0 }-> a__incr(1 + z0 + (1 + z1)) :|: z = 1 + (1 + z015 + z11), z015 >= 0, z11 >= 0, z1 >= 0, z0 >= 0, 1 + z015 + z11 = 1 + z0 + z1 mark(z) -{ 0 }-> a__incr(1 + z0 + (1 + z1)) :|: z016 >= 0, z = 1 + (1 + z016), z1 >= 0, z0 >= 0, 1 + z016 = 1 + z0 + z1 mark(z) -{ 0 }-> a__incr(1 + z0 + (1 + z1)) :|: z = 1 + 2, z1 >= 0, z0 >= 0, 1 + 0 + 2 = 1 + z0 + z1 mark(z) -{ 0 }-> a__incr(1 + z0 + (1 + z1)) :|: z = 1 + 2, z1 >= 0, z0 >= 0, 2 = 1 + z0 + z1 mark(z) -{ 0 }-> a__hd(a__tl(mark(z026))) :|: z = 1 + (1 + z026), z026 >= 0 mark(z) -{ 0 }-> a__hd(a__nats) :|: z = 1 + 1 mark(z) -{ 0 }-> a__hd(a__incr(mark(z024))) :|: z024 >= 0, z = 1 + (1 + z024) mark(z) -{ 0 }-> a__hd(a__hd(mark(z025))) :|: z025 >= 0, z = 1 + (1 + z025) mark(z) -{ 0 }-> a__hd(a__adx(mark(z023))) :|: z023 >= 0, z = 1 + (1 + z023) mark(z) -{ 0 }-> a__hd(2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__hd(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__hd(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__hd(0) :|: z = 1 + 2 mark(z) -{ 0 }-> a__hd(1 + z028) :|: z028 >= 0, z = 1 + (1 + z028) mark(z) -{ 0 }-> a__hd(1 + z027 + z13) :|: z027 >= 0, z = 1 + (1 + z027 + z13), z13 >= 0 mark(z) -{ 0 }-> a__hd(1 + 0 + 2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__adx(a__tl(mark(z014))) :|: z = 1 + (1 + z014), z014 >= 0 mark(z) -{ 0 }-> a__adx(a__nats) :|: z = 1 + 1 mark(z) -{ 0 }-> a__adx(a__incr(mark(z012))) :|: z012 >= 0, z = 1 + (1 + z012) mark(z) -{ 0 }-> a__adx(a__hd(mark(z013))) :|: z013 >= 0, z = 1 + (1 + z013) mark(z) -{ 0 }-> a__adx(a__adx(mark(z011))) :|: z = 1 + (1 + z011), z011 >= 0 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 0 :|: z = 2 mark(z) -{ 0 }-> 0 :|: z021 >= 0, z = 1 + (1 + z021 + z12), z12 >= 0, v0 >= 0, 1 + z021 + z12 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 0 :|: z022 >= 0, z = 1 + (1 + z022), v0 >= 0, 1 + z022 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 + 0 + 2 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + (1 + z015 + z11), z015 >= 0, z11 >= 0, v0 >= 0, 1 + z015 + z11 = v0 mark(z) -{ 0 }-> 0 :|: z016 >= 0, z = 1 + (1 + z016), v0 >= 0, 1 + z016 = v0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z021 >= 0, z = 1 + (1 + z021 + z12), z12 >= 0, 1 + z021 + z12 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z022 >= 0, z = 1 + (1 + z022), 1 + z022 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 2, 1 + 0 + 2 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 2, 0 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 2, 2 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + (1 + z015 + z11), z015 >= 0, z11 >= 0, 1 + z015 + z11 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z016 >= 0, z = 1 + (1 + z016), 1 + z016 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0' :|: z = 1 + z0, z0 >= 0, 0 = z0', z0' >= 0 mark(z) -{ 0 }-> 1 + z0 + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + 0 + 2 :|: z = 2 mark(z) -{ 0 }-> 1 + (1 + z0) + (1 + z1) :|: z021 >= 0, z = 1 + (1 + z021 + z12), z12 >= 0, z1 >= 0, z0 >= 0, 1 + z021 + z12 = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + (1 + z0) + (1 + z1) :|: z022 >= 0, z = 1 + (1 + z022), z1 >= 0, z0 >= 0, 1 + z022 = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + (1 + z0) + (1 + z1) :|: z = 1 + 2, z1 >= 0, z0 >= 0, 1 + 0 + 2 = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + (1 + z0) + (1 + z1) :|: z = 1 + 2, z1 >= 0, z0 >= 0, 2 = 1 + z0 + z1 ---------------------------------------- (39) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (40) Obligation: Complexity RNTS consisting of the following rules: A__HD(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TL(z) -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__TL(a__tl(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__TL(a__nats) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__TL(a__incr(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__TL(a__hd(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__TL(a__adx(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__TL(2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__TL(0) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__TL(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__TL(0) + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__TL(1 + (z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__TL(1 + z09 + z1'') + MARK(1 + z09 + z1'') :|: z = 1 + (1 + z09 + z1''), z09 >= 0, z1'' >= 0 MARK(z) -{ 1 }-> 1 + A__TL(1 + 0 + 2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__HD(a__tl(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__HD(a__nats) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__HD(a__incr(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__HD(a__hd(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__HD(a__adx(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__HD(2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__HD(0) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__HD(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__HD(0) + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__HD(1 + (z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__HD(1 + z03 + z1') + MARK(1 + z03 + z1') :|: z1' >= 0, z03 >= 0, z = 1 + (1 + z03 + z1') MARK(z) -{ 1 }-> 1 + A__HD(1 + 0 + 2) + MARK(2) :|: z = 1 + 2 a__adx(z) -{ 0 }-> 0 :|: z >= 0 a__adx(z) -{ 0 }-> 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, 1 + z0 + (1 + z1) = v0 a__adx(z) -{ 0 }-> 1 + z :|: z >= 0 a__adx(z) -{ 0 }-> 1 + z0' :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, 1 + z0 + (1 + z1) = z0', z0' >= 0 a__adx(z) -{ 0 }-> 1 + (1 + z0') + (1 + z1') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + z0 + (1 + z1) = 1 + z0' + z1' a__hd(z) -{ 0 }-> mark(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__hd(z) -{ 0 }-> 0 :|: z >= 0 a__hd(z) -{ 0 }-> 1 + z :|: z >= 0 a__incr(z) -{ 0 }-> 0 :|: z >= 0 a__incr(z) -{ 0 }-> 1 + z :|: z >= 0 a__incr(z) -{ 0 }-> 1 + (1 + z0) + (1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__nats -{ 0 }-> a__incr(1 + z0 + (1 + z1)) :|: z1 >= 0, z0 >= 0, 1 + 0 + 2 = 1 + z0 + z1 a__nats -{ 0 }-> a__incr(1 + z0 + (1 + z1)) :|: z1 >= 0, z0 >= 0, 2 = 1 + z0 + z1 a__nats -{ 0 }-> 1 :|: a__nats -{ 0 }-> 0 :|: a__nats -{ 0 }-> 0 :|: v0 >= 0, 1 + 0 + 2 = v0 a__nats -{ 0 }-> 0 :|: v0 >= 0, 2 = v0 a__nats -{ 0 }-> 0 :|: v0 >= 0, 0 = v0 a__nats -{ 0 }-> 1 + z0 :|: 1 + 0 + 2 = z0, z0 >= 0 a__nats -{ 0 }-> 1 + z0 :|: 2 = z0, z0 >= 0 a__nats -{ 0 }-> 1 + z0 :|: 0 = z0, z0 >= 0 a__tl(z) -{ 0 }-> mark(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__tl(z) -{ 0 }-> 0 :|: z >= 0 a__tl(z) -{ 0 }-> 1 + z :|: z >= 0 a__zeros -{ 0 }-> 2 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 2 :|: mark(z) -{ 0 }-> a__tl(a__tl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__tl(a__nats) :|: z = 1 + 1 mark(z) -{ 0 }-> a__tl(a__incr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__tl(a__hd(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__tl(a__adx(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__tl(2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__tl(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__tl(0) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__tl(0) :|: z = 1 + 2 mark(z) -{ 0 }-> a__tl(1 + (z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__tl(1 + z033 + z14) :|: z = 1 + (1 + z033 + z14), z033 >= 0, z14 >= 0 mark(z) -{ 0 }-> a__tl(1 + 0 + 2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__nats :|: z = 1 mark(z) -{ 0 }-> a__incr(a__tl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__incr(a__nats) :|: z = 1 + 1 mark(z) -{ 0 }-> a__incr(a__incr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__incr(a__hd(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__incr(a__adx(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__incr(1 + z0 + (1 + z1)) :|: z = 1 + (1 + z015 + z11), z015 >= 0, z11 >= 0, z1 >= 0, z0 >= 0, 1 + z015 + z11 = 1 + z0 + z1 mark(z) -{ 0 }-> a__incr(1 + z0 + (1 + z1)) :|: z - 2 >= 0, z1 >= 0, z0 >= 0, 1 + (z - 2) = 1 + z0 + z1 mark(z) -{ 0 }-> a__incr(1 + z0 + (1 + z1)) :|: z = 1 + 2, z1 >= 0, z0 >= 0, 1 + 0 + 2 = 1 + z0 + z1 mark(z) -{ 0 }-> a__incr(1 + z0 + (1 + z1)) :|: z = 1 + 2, z1 >= 0, z0 >= 0, 2 = 1 + z0 + z1 mark(z) -{ 0 }-> a__hd(a__tl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__hd(a__nats) :|: z = 1 + 1 mark(z) -{ 0 }-> a__hd(a__incr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__hd(a__hd(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__hd(a__adx(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__hd(2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__hd(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__hd(0) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__hd(0) :|: z = 1 + 2 mark(z) -{ 0 }-> a__hd(1 + (z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__hd(1 + z027 + z13) :|: z027 >= 0, z = 1 + (1 + z027 + z13), z13 >= 0 mark(z) -{ 0 }-> a__hd(1 + 0 + 2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__adx(a__tl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__adx(a__nats) :|: z = 1 + 1 mark(z) -{ 0 }-> a__adx(a__incr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__adx(a__hd(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__adx(a__adx(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: z >= 0 mark(z) -{ 0 }-> 0 :|: z = 2 mark(z) -{ 0 }-> 0 :|: z021 >= 0, z = 1 + (1 + z021 + z12), z12 >= 0, v0 >= 0, 1 + z021 + z12 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 0 :|: z - 2 >= 0, v0 >= 0, 1 + (z - 2) = v0 mark(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 + 0 + 2 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + (1 + z015 + z11), z015 >= 0, z11 >= 0, v0 >= 0, 1 + z015 + z11 = v0 mark(z) -{ 0 }-> 1 + z0 :|: z021 >= 0, z = 1 + (1 + z021 + z12), z12 >= 0, 1 + z021 + z12 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z - 2 >= 0, 1 + (z - 2) = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 2, 1 + 0 + 2 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 2, 0 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 2, 2 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + (1 + z015 + z11), z015 >= 0, z11 >= 0, 1 + z015 + z11 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0 mark(z) -{ 0 }-> 1 + (z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> 1 + z0 + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + 0 + 2 :|: z = 2 mark(z) -{ 0 }-> 1 + (1 + z0) + (1 + z1) :|: z021 >= 0, z = 1 + (1 + z021 + z12), z12 >= 0, z1 >= 0, z0 >= 0, 1 + z021 + z12 = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + (1 + z0) + (1 + z1) :|: z - 2 >= 0, z1 >= 0, z0 >= 0, 1 + (z - 2) = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + (1 + z0) + (1 + z1) :|: z = 1 + 2, z1 >= 0, z0 >= 0, 1 + 0 + 2 = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + (1 + z0) + (1 + z1) :|: z = 1 + 2, z1 >= 0, z0 >= 0, 2 = 1 + z0 + z1 ---------------------------------------- (41) 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__nats -> null_a__nats [0] a__zeros -> null_a__zeros [0] a__incr(v0) -> null_a__incr [0] a__adx(v0) -> null_a__adx [0] a__hd(v0) -> null_a__hd [0] a__tl(v0) -> null_a__tl [0] mark(v0) -> null_mark [0] A__HD(v0) -> null_A__HD [0] A__TL(v0) -> null_A__TL [0] MARK(v0) -> null_MARK [0] And the following fresh constants: null_a__nats, null_a__zeros, null_a__incr, null_a__adx, null_a__hd, null_a__tl, null_mark, null_A__HD, null_A__TL, null_MARK ---------------------------------------- (42) 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__HD(cons(z0, z1)) -> c8(MARK(z0)) [1] A__TL(cons(z0, z1)) -> c10(MARK(z1)) [1] MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) [1] MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) [1] MARK(adx(z0)) -> c13(MARK(z0)) [1] MARK(incr(z0)) -> c15(MARK(z0)) [1] a__nats -> a__adx(a__zeros) [0] a__nats -> nats [0] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) [0] a__incr(z0) -> incr(z0) [0] a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) [0] a__adx(z0) -> adx(z0) [0] a__hd(cons(z0, z1)) -> mark(z0) [0] a__hd(z0) -> hd(z0) [0] a__tl(cons(z0, z1)) -> mark(z1) [0] a__tl(z0) -> tl(z0) [0] mark(nats) -> a__nats [0] mark(adx(z0)) -> a__adx(mark(z0)) [0] mark(zeros) -> a__zeros [0] mark(incr(z0)) -> a__incr(mark(z0)) [0] mark(hd(z0)) -> a__hd(mark(z0)) [0] mark(tl(z0)) -> a__tl(mark(z0)) [0] mark(cons(z0, z1)) -> cons(z0, z1) [0] mark(0) -> 0 [0] mark(s(z0)) -> s(z0) [0] a__nats -> null_a__nats [0] a__zeros -> null_a__zeros [0] a__incr(v0) -> null_a__incr [0] a__adx(v0) -> null_a__adx [0] a__hd(v0) -> null_a__hd [0] a__tl(v0) -> null_a__tl [0] mark(v0) -> null_mark [0] A__HD(v0) -> null_A__HD [0] A__TL(v0) -> null_A__TL [0] MARK(v0) -> null_MARK [0] The TRS has the following type information: A__HD :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> c8:null_A__HD cons :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark c8 :: c16:c17:c13:c15:null_MARK -> c8:null_A__HD MARK :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> c16:c17:c13:c15:null_MARK A__TL :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> c10:null_A__TL c10 :: c16:c17:c13:c15:null_MARK -> c10:null_A__TL hd :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark c16 :: c8:null_A__HD -> c16:c17:c13:c15:null_MARK -> c16:c17:c13:c15:null_MARK mark :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark tl :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark c17 :: c10:null_A__TL -> c16:c17:c13:c15:null_MARK -> c16:c17:c13:c15:null_MARK adx :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark c13 :: c16:c17:c13:c15:null_MARK -> c16:c17:c13:c15:null_MARK incr :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark c15 :: c16:c17:c13:c15:null_MARK -> c16:c17:c13:c15:null_MARK a__nats :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark a__adx :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark a__zeros :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark nats :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark 0 :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark zeros :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark a__incr :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark s :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark a__hd :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark a__tl :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark -> cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__nats :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__zeros :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__incr :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__adx :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__hd :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_a__tl :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_mark :: cons:hd:tl:adx:incr:nats:0:zeros:s:null_a__nats:null_a__zeros:null_a__incr:null_a__adx:null_a__hd:null_a__tl:null_mark null_A__HD :: c8:null_A__HD null_A__TL :: c10:null_A__TL null_MARK :: c16:c17:c13:c15:null_MARK Rewrite Strategy: INNERMOST ---------------------------------------- (43) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: nats => 1 0 => 0 zeros => 2 null_a__nats => 0 null_a__zeros => 0 null_a__incr => 0 null_a__adx => 0 null_a__hd => 0 null_a__tl => 0 null_mark => 0 null_A__HD => 0 null_A__TL => 0 null_MARK => 0 ---------------------------------------- (44) Obligation: Complexity RNTS consisting of the following rules: A__HD(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__HD(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TL(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__TL(z) -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__TL(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__HD(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 a__adx(z) -{ 0 }-> a__incr(1 + z0 + (1 + z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__adx(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__adx(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__hd(z) -{ 0 }-> mark(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__hd(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__hd(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__incr(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__incr(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__incr(z) -{ 0 }-> 1 + (1 + z0) + (1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__nats -{ 0 }-> a__adx(a__zeros) :|: a__nats -{ 0 }-> 1 :|: a__nats -{ 0 }-> 0 :|: a__tl(z) -{ 0 }-> mark(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__tl(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__tl(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__zeros -{ 0 }-> 2 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 2 :|: mark(z) -{ 0 }-> a__zeros :|: z = 2 mark(z) -{ 0 }-> a__tl(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__nats :|: z = 1 mark(z) -{ 0 }-> a__incr(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__hd(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__adx(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (45) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(hd(z0)) -> c16(A__HD(mark(z0)), MARK(z0)) by MARK(hd(nats)) -> c16(A__HD(a__nats), MARK(nats)) MARK(hd(adx(z0))) -> c16(A__HD(a__adx(mark(z0))), MARK(adx(z0))) MARK(hd(zeros)) -> c16(A__HD(a__zeros), MARK(zeros)) MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1)), MARK(cons(z0, z1))) MARK(hd(0)) -> c16(A__HD(0), MARK(0)) MARK(hd(s(z0))) -> c16(A__HD(s(z0)), MARK(s(z0))) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(nats)) -> c16(A__HD(a__nats), MARK(nats)) MARK(hd(adx(z0))) -> c16(A__HD(a__adx(mark(z0))), MARK(adx(z0))) MARK(hd(zeros)) -> c16(A__HD(a__zeros), MARK(zeros)) MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1)), MARK(cons(z0, z1))) MARK(hd(0)) -> c16(A__HD(0), MARK(0)) MARK(hd(s(z0))) -> c16(A__HD(s(z0)), MARK(s(z0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(nats)) -> c16(A__HD(a__nats), MARK(nats)) MARK(hd(adx(z0))) -> c16(A__HD(a__adx(mark(z0))), MARK(adx(z0))) MARK(hd(zeros)) -> c16(A__HD(a__zeros), MARK(zeros)) MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1)), MARK(cons(z0, z1))) MARK(hd(0)) -> c16(A__HD(0), MARK(0)) MARK(hd(s(z0))) -> c16(A__HD(s(z0)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c17_2, c13_1, c15_1, c16_2 ---------------------------------------- (47) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(hd(s(z0))) -> c16(A__HD(s(z0)), MARK(s(z0))) MARK(hd(0)) -> c16(A__HD(0), MARK(0)) ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(nats)) -> c16(A__HD(a__nats), MARK(nats)) MARK(hd(adx(z0))) -> c16(A__HD(a__adx(mark(z0))), MARK(adx(z0))) MARK(hd(zeros)) -> c16(A__HD(a__zeros), MARK(zeros)) MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1)), MARK(cons(z0, z1))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(nats)) -> c16(A__HD(a__nats), MARK(nats)) MARK(hd(adx(z0))) -> c16(A__HD(a__adx(mark(z0))), MARK(adx(z0))) MARK(hd(zeros)) -> c16(A__HD(a__zeros), MARK(zeros)) MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1)), MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c17_2, c13_1, c15_1, c16_2 ---------------------------------------- (49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(adx(z0))) -> c16(A__HD(a__adx(mark(z0))), MARK(adx(z0))) MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(adx(z0))) -> c16(A__HD(a__adx(mark(z0))), MARK(adx(z0))) MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c17_2, c13_1, c15_1, c16_2, c16_1 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(tl(z0)) -> c17(A__TL(mark(z0)), MARK(z0)) by MARK(tl(nats)) -> c17(A__TL(a__nats), MARK(nats)) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(zeros)) -> c17(A__TL(a__zeros), MARK(zeros)) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1)), MARK(cons(z0, z1))) MARK(tl(0)) -> c17(A__TL(0), MARK(0)) MARK(tl(s(z0))) -> c17(A__TL(s(z0)), MARK(s(z0))) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(adx(z0))) -> c16(A__HD(a__adx(mark(z0))), MARK(adx(z0))) MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(nats)) -> c17(A__TL(a__nats), MARK(nats)) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(zeros)) -> c17(A__TL(a__zeros), MARK(zeros)) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1)), MARK(cons(z0, z1))) MARK(tl(0)) -> c17(A__TL(0), MARK(0)) MARK(tl(s(z0))) -> c17(A__TL(s(z0)), MARK(s(z0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(adx(z0))) -> c16(A__HD(a__adx(mark(z0))), MARK(adx(z0))) MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(nats)) -> c17(A__TL(a__nats), MARK(nats)) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(zeros)) -> c17(A__TL(a__zeros), MARK(zeros)) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1)), MARK(cons(z0, z1))) MARK(tl(0)) -> c17(A__TL(0), MARK(0)) MARK(tl(s(z0))) -> c17(A__TL(s(z0)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_2, c16_1, c17_2 ---------------------------------------- (53) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(tl(s(z0))) -> c17(A__TL(s(z0)), MARK(s(z0))) MARK(tl(0)) -> c17(A__TL(0), MARK(0)) ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(adx(z0))) -> c16(A__HD(a__adx(mark(z0))), MARK(adx(z0))) MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(nats)) -> c17(A__TL(a__nats), MARK(nats)) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(zeros)) -> c17(A__TL(a__zeros), MARK(zeros)) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1)), MARK(cons(z0, z1))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(adx(z0))) -> c16(A__HD(a__adx(mark(z0))), MARK(adx(z0))) MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(nats)) -> c17(A__TL(a__nats), MARK(nats)) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(zeros)) -> c17(A__TL(a__zeros), MARK(zeros)) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1)), MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_2, c16_1, c17_2 ---------------------------------------- (55) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(adx(z0))) -> c16(A__HD(a__adx(mark(z0))), MARK(adx(z0))) MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(adx(z0))) -> c16(A__HD(a__adx(mark(z0))), MARK(adx(z0))) MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (57) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(hd(adx(z0))) -> c16(A__HD(a__adx(mark(z0))), MARK(adx(z0))) by MARK(hd(adx(x0))) -> c16(A__HD(adx(mark(x0))), MARK(adx(x0))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(x0))) -> c16(A__HD(adx(mark(x0))), MARK(adx(x0))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(x0))) -> c16(A__HD(adx(mark(x0))), MARK(adx(x0))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(hd(incr(z0))) -> c16(A__HD(a__incr(mark(z0))), MARK(incr(z0))) by MARK(hd(incr(x0))) -> c16(A__HD(incr(mark(x0))), MARK(incr(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(x0))) -> c16(A__HD(incr(mark(x0))), MARK(incr(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(x0))) -> c16(A__HD(incr(mark(x0))), MARK(incr(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(hd(hd(z0))) -> c16(A__HD(a__hd(mark(z0))), MARK(hd(z0))) by MARK(hd(hd(x0))) -> c16(A__HD(hd(mark(x0))), MARK(hd(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0)), MARK(hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0))), MARK(hd(s(z0)))) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(x0))) -> c16(A__HD(hd(mark(x0))), MARK(hd(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0)), MARK(hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0))), MARK(hd(s(z0)))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(x0))) -> c16(A__HD(hd(mark(x0))), MARK(hd(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0)), MARK(hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0))), MARK(hd(s(z0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(hd(tl(z0))) -> c16(A__HD(a__tl(mark(z0))), MARK(tl(z0))) by MARK(hd(tl(x0))) -> c16(A__HD(tl(mark(x0))), MARK(tl(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0)), MARK(tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0))), MARK(tl(s(z0)))) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(x0))) -> c16(A__HD(tl(mark(x0))), MARK(tl(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0)), MARK(tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0))), MARK(tl(s(z0)))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(x0))) -> c16(A__HD(tl(mark(x0))), MARK(tl(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0)), MARK(tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0))), MARK(tl(s(z0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_2, c17_1, c16_2 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(nats)) -> c16(A__HD(a__nats)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_2, c17_1, c16_2 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(hd(nats)) -> c16(A__HD(a__nats)) by MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(nats)) -> c16(A__HD(nats)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(nats)) -> c16(A__HD(nats)) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(nats)) -> c16(A__HD(nats)) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_2, c17_1, c16_2 ---------------------------------------- (75) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(hd(nats)) -> c16(A__HD(nats)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(zeros)) -> c16(A__HD(a__zeros)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_2, c17_1, c16_2 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(hd(zeros)) -> c16(A__HD(a__zeros)) by MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(hd(zeros)) -> c16(A__HD(zeros)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(hd(zeros)) -> c16(A__HD(zeros)) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(hd(zeros)) -> c16(A__HD(zeros)) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_2, c17_1, c16_2 ---------------------------------------- (79) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(hd(zeros)) -> c16(A__HD(zeros)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_2, c17_1, c16_2 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(tl(adx(z0))) -> c17(A__TL(a__adx(mark(z0))), MARK(adx(z0))) by MARK(tl(adx(x0))) -> c17(A__TL(adx(mark(x0))), MARK(adx(x0))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(x0))) -> c17(A__TL(adx(mark(x0))), MARK(adx(x0))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(x0))) -> c17(A__TL(adx(mark(x0))), MARK(adx(x0))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_2, c17_1, c16_2 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_2, c17_1, c16_2 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(tl(incr(z0))) -> c17(A__TL(a__incr(mark(z0))), MARK(incr(z0))) by MARK(tl(incr(x0))) -> c17(A__TL(incr(mark(x0))), MARK(incr(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(x0))) -> c17(A__TL(incr(mark(x0))), MARK(incr(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(x0))) -> c17(A__TL(incr(mark(x0))), MARK(incr(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_2, c17_1, c16_2 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_2, c17_1, c16_2 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(tl(hd(z0))) -> c17(A__TL(a__hd(mark(z0))), MARK(hd(z0))) by MARK(tl(hd(x0))) -> c17(A__TL(hd(mark(x0))), MARK(hd(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0)), MARK(hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0))), MARK(hd(s(z0)))) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(x0))) -> c17(A__TL(hd(mark(x0))), MARK(hd(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0)), MARK(hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0))), MARK(hd(s(z0)))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(x0))) -> c17(A__TL(hd(mark(x0))), MARK(hd(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0)), MARK(hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0))), MARK(hd(s(z0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_2, c17_1, c16_2 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_2, c17_1, c16_2 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(tl(tl(z0))) -> c17(A__TL(a__tl(mark(z0))), MARK(tl(z0))) by MARK(tl(tl(x0))) -> c17(A__TL(tl(mark(x0))), MARK(tl(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0)), MARK(tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0))), MARK(tl(s(z0)))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(x0))) -> c17(A__TL(tl(mark(x0))), MARK(tl(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0)), MARK(tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0))), MARK(tl(s(z0)))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(x0))) -> c17(A__TL(tl(mark(x0))), MARK(tl(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0)), MARK(tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0))), MARK(tl(s(z0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(nats)) -> c17(A__TL(a__nats)) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(tl(nats)) -> c17(A__TL(a__nats)) by MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(nats)) -> c17(A__TL(nats)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(nats)) -> c17(A__TL(nats)) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(nats)) -> c17(A__TL(nats)) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (99) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(tl(nats)) -> c17(A__TL(nats)) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(zeros)) -> c17(A__TL(a__zeros)) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(tl(zeros)) -> c17(A__TL(a__zeros)) by MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(tl(zeros)) -> c17(A__TL(zeros)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(tl(zeros)) -> c17(A__TL(zeros)) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(tl(zeros)) -> c17(A__TL(zeros)) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(tl(zeros)) -> c17(A__TL(zeros)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(hd(hd(0))) -> c16(A__HD(a__hd(0))) by MARK(hd(hd(0))) -> c16(A__HD(hd(0))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(hd(0))) -> c16(A__HD(hd(0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(hd(0))) -> c16(A__HD(hd(0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(hd(hd(0))) -> c16(A__HD(hd(0))) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(hd(hd(s(z0)))) -> c16(A__HD(a__hd(s(z0)))) by MARK(hd(hd(s(x0)))) -> c16(A__HD(hd(s(x0)))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(hd(s(x0)))) -> c16(A__HD(hd(s(x0)))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(hd(s(x0)))) -> c16(A__HD(hd(s(x0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(hd(hd(s(x0)))) -> c16(A__HD(hd(s(x0)))) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(hd(tl(0))) -> c16(A__HD(a__tl(0))) by MARK(hd(tl(0))) -> c16(A__HD(tl(0))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(tl(0))) -> c16(A__HD(tl(0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(tl(0))) -> c16(A__HD(tl(0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(hd(tl(0))) -> c16(A__HD(tl(0))) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(hd(tl(s(z0)))) -> c16(A__HD(a__tl(s(z0)))) by MARK(hd(tl(s(x0)))) -> c16(A__HD(tl(s(x0)))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(tl(s(x0)))) -> c16(A__HD(tl(s(x0)))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(tl(s(x0)))) -> c16(A__HD(tl(s(x0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(hd(tl(s(x0)))) -> c16(A__HD(tl(s(x0)))) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(tl(hd(0))) -> c17(A__TL(a__hd(0))) by MARK(tl(hd(0))) -> c17(A__TL(hd(0))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(tl(hd(0))) -> c17(A__TL(hd(0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(tl(hd(0))) -> c17(A__TL(hd(0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (123) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(tl(hd(0))) -> c17(A__TL(hd(0))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(tl(hd(s(z0)))) -> c17(A__TL(a__hd(s(z0)))) by MARK(tl(hd(s(x0)))) -> c17(A__TL(hd(s(x0)))) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(tl(hd(s(x0)))) -> c17(A__TL(hd(s(x0)))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(tl(hd(s(x0)))) -> c17(A__TL(hd(s(x0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (127) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(tl(hd(s(x0)))) -> c17(A__TL(hd(s(x0)))) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (129) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(tl(tl(0))) -> c17(A__TL(a__tl(0))) by MARK(tl(tl(0))) -> c17(A__TL(tl(0))) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(tl(tl(0))) -> c17(A__TL(tl(0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(tl(tl(0))) -> c17(A__TL(tl(0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (131) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(tl(tl(0))) -> c17(A__TL(tl(0))) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (133) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(tl(tl(s(z0)))) -> c17(A__TL(a__tl(s(z0)))) by MARK(tl(tl(s(x0)))) -> c17(A__TL(tl(s(x0)))) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(tl(tl(s(x0)))) -> c17(A__TL(tl(s(x0)))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(tl(tl(s(x0)))) -> c17(A__TL(tl(s(x0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (135) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(tl(tl(s(x0)))) -> c17(A__TL(tl(s(x0)))) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (137) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace MARK(hd(adx(0))) -> c16(A__HD(a__adx(0)), MARK(adx(0))) by MARK(hd(adx(0))) -> c16(A__HD(adx(0)), MARK(adx(0))) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(A__HD(adx(0)), MARK(adx(0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(A__HD(adx(0)), MARK(adx(0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (141) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace MARK(hd(adx(s(z0)))) -> c16(A__HD(a__adx(s(z0))), MARK(adx(s(z0)))) by MARK(hd(adx(s(z0)))) -> c16(A__HD(adx(s(z0))), MARK(adx(s(z0)))) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(adx(s(z0))), MARK(adx(s(z0)))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(A__HD(adx(s(z0))), MARK(adx(s(z0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (145) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace MARK(hd(incr(0))) -> c16(A__HD(a__incr(0)), MARK(incr(0))) by MARK(hd(incr(0))) -> c16(A__HD(incr(0)), MARK(incr(0))) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(A__HD(incr(0)), MARK(incr(0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(A__HD(incr(0)), MARK(incr(0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (147) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (149) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace MARK(hd(incr(s(z0)))) -> c16(A__HD(a__incr(s(z0))), MARK(incr(s(z0)))) by MARK(hd(incr(s(z0)))) -> c16(A__HD(incr(s(z0))), MARK(incr(s(z0)))) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(incr(s(z0))), MARK(incr(s(z0)))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(A__HD(incr(s(z0))), MARK(incr(s(z0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) S tuples: A__HD(cons(z0, z1)) -> c8(MARK(z0)) A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__HD_1, A__TL_1, MARK_1 Compound Symbols: c8_1, c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2 ---------------------------------------- (153) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A__HD(cons(z0, z1)) -> c8(MARK(z0)) by A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(hd(zeros), z1)) -> c8(MARK(hd(zeros))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(tl(zeros), z1)) -> c8(MARK(tl(zeros))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(hd(zeros), z1)) -> c8(MARK(hd(zeros))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(tl(zeros), z1)) -> c8(MARK(tl(zeros))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) S tuples: A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(hd(zeros), z1)) -> c8(MARK(hd(zeros))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(tl(zeros), z1)) -> c8(MARK(tl(zeros))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__TL_1, MARK_1, A__HD_1 Compound Symbols: c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2, c8_1 ---------------------------------------- (155) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(hd(zeros)) -> c16(A__HD(cons(0, zeros))) A__HD(cons(hd(zeros), z1)) -> c8(MARK(hd(zeros))) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(tl(zeros), z1)) -> c8(MARK(tl(zeros))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) S tuples: A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros)), MARK(hd(zeros))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros)), MARK(hd(zeros))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(tl(zeros), z1)) -> c8(MARK(tl(zeros))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__TL_1, MARK_1, A__HD_1 Compound Symbols: c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2, c8_1 ---------------------------------------- (157) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(tl(zeros), z1)) -> c8(MARK(tl(zeros))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) S tuples: A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(tl(zeros), z1)) -> c8(MARK(tl(zeros))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__TL_1, MARK_1, A__HD_1 Compound Symbols: c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2, c8_1 ---------------------------------------- (159) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace MARK(tl(adx(0))) -> c17(A__TL(a__adx(0)), MARK(adx(0))) by MARK(tl(adx(0))) -> c17(A__TL(adx(0)), MARK(adx(0))) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(tl(zeros), z1)) -> c8(MARK(tl(zeros))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(A__TL(adx(0)), MARK(adx(0))) S tuples: A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(tl(zeros), z1)) -> c8(MARK(tl(zeros))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(A__TL(adx(0)), MARK(adx(0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__TL_1, MARK_1, A__HD_1 Compound Symbols: c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2, c8_1 ---------------------------------------- (161) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(tl(zeros), z1)) -> c8(MARK(tl(zeros))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) S tuples: A__TL(cons(z0, z1)) -> c10(MARK(z1)) MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(tl(zeros), z1)) -> c8(MARK(tl(zeros))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: A__TL_1, MARK_1, A__HD_1 Compound Symbols: c10_1, c13_1, c15_1, c16_1, c17_1, c16_2, c17_2, c8_1 ---------------------------------------- (163) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A__TL(cons(z0, z1)) -> c10(MARK(z1)) by A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, tl(zeros))) -> c10(MARK(tl(zeros))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(tl(zeros), z1)) -> c8(MARK(tl(zeros))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, tl(zeros))) -> c10(MARK(tl(zeros))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) S tuples: MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(tl(zeros), z1)) -> c8(MARK(tl(zeros))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, tl(zeros))) -> c10(MARK(tl(zeros))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c13_1, c15_1, c16_1, c17_1, c16_2, c17_2, c8_1, c10_1 ---------------------------------------- (165) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: A__TL(cons(z0, tl(zeros))) -> c10(MARK(tl(zeros))) A__HD(cons(tl(zeros), z1)) -> c8(MARK(tl(zeros))) MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) S tuples: MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros)), MARK(tl(zeros))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros)), MARK(tl(zeros))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c13_1, c15_1, c16_1, c17_1, c16_2, c17_2, c8_1, c10_1 ---------------------------------------- (167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) S tuples: MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c13_1, c15_1, c16_1, c17_1, c16_2, c17_2, c8_1, c10_1 ---------------------------------------- (169) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0))), MARK(adx(s(z0)))) by MARK(tl(adx(s(z0)))) -> c17(A__TL(adx(s(z0))), MARK(adx(s(z0)))) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(adx(s(z0)))) -> c17(A__TL(adx(s(z0))), MARK(adx(s(z0)))) S tuples: MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(adx(s(z0)))) -> c17(A__TL(adx(s(z0))), MARK(adx(s(z0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c13_1, c15_1, c16_1, c17_1, c16_2, c17_2, c8_1, c10_1 ---------------------------------------- (171) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(adx(s(z0)))) -> c17(MARK(adx(s(z0)))) S tuples: MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(adx(s(z0)))) -> c17(MARK(adx(s(z0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c13_1, c15_1, c16_1, c17_1, c16_2, c17_2, c8_1, c10_1 ---------------------------------------- (173) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace MARK(tl(incr(0))) -> c17(A__TL(a__incr(0)), MARK(incr(0))) by MARK(tl(incr(0))) -> c17(A__TL(incr(0)), MARK(incr(0))) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(adx(s(z0)))) -> c17(MARK(adx(s(z0)))) MARK(tl(incr(0))) -> c17(A__TL(incr(0)), MARK(incr(0))) S tuples: MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) 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MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> 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tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(adx(s(z0)))) -> c17(MARK(adx(s(z0)))) MARK(tl(incr(0))) -> c17(A__TL(incr(0)), MARK(incr(0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c13_1, c15_1, c16_1, c17_1, c16_2, c17_2, c8_1, c10_1 ---------------------------------------- (175) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(adx(s(z0)))) -> c17(MARK(adx(s(z0)))) MARK(tl(incr(0))) -> c17(MARK(incr(0))) S tuples: MARK(adx(z0)) -> c13(MARK(z0)) MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(adx(s(z0)))) -> c17(MARK(adx(s(z0)))) MARK(tl(incr(0))) -> c17(MARK(incr(0))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c13_1, c15_1, c16_1, c17_1, c16_2, c17_2, c8_1, c10_1 ---------------------------------------- (177) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(adx(z0)) -> c13(MARK(z0)) by MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(adx(s(z0)))) -> c17(MARK(adx(s(z0)))) MARK(tl(incr(0))) -> c17(MARK(incr(0))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) S tuples: MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> 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A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) 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c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(adx(s(z0)))) -> c17(MARK(adx(s(z0)))) MARK(tl(incr(0))) -> c17(MARK(incr(0))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c15_1, c16_1, c17_1, c16_2, c17_2, c8_1, c10_1, c13_1 ---------------------------------------- (179) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing nodes: MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) MARK(tl(adx(s(z0)))) -> c17(MARK(adx(s(z0)))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(incr(0))) -> c17(MARK(incr(0))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) S tuples: MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats)), MARK(adx(nats))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros)), MARK(adx(zeros))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats)), MARK(adx(nats))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros)), MARK(adx(zeros))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1))), MARK(adx(cons(z0, z1)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(incr(0))) -> c17(MARK(incr(0))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c15_1, c16_1, c17_1, c16_2, c17_2, c8_1, c10_1, c13_1 ---------------------------------------- (181) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, 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c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, 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c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) S tuples: MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(incr(0))) -> c17(MARK(incr(0))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c15_1, c16_1, c17_1, c16_2, c17_2, c8_1, c10_1, c13_1 ---------------------------------------- (183) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace MARK(tl(incr(s(z0)))) -> c17(A__TL(a__incr(s(z0))), MARK(incr(s(z0)))) by MARK(tl(incr(s(z0)))) -> c17(A__TL(incr(s(z0))), MARK(incr(s(z0)))) ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(incr(0))) -> c17(MARK(incr(0))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(tl(incr(s(z0)))) -> c17(A__TL(incr(s(z0))), MARK(incr(s(z0)))) S tuples: MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(incr(0))) -> c17(MARK(incr(0))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(tl(incr(s(z0)))) -> c17(A__TL(incr(s(z0))), MARK(incr(s(z0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c15_1, c16_1, c17_1, c16_2, c17_2, c8_1, c10_1, c13_1 ---------------------------------------- (185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(incr(0))) -> c17(MARK(incr(0))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(tl(incr(s(z0)))) -> c17(MARK(incr(s(z0)))) S tuples: MARK(incr(z0)) -> c15(MARK(z0)) MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, 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A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(incr(0))) -> c17(MARK(incr(0))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(tl(incr(s(z0)))) -> c17(MARK(incr(s(z0)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c15_1, c16_1, c17_1, c16_2, c17_2, c8_1, c10_1, c13_1 ---------------------------------------- (187) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(incr(z0)) -> c15(MARK(z0)) by MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(incr(0))) -> c17(MARK(incr(0))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(tl(incr(s(z0)))) -> c17(MARK(incr(s(z0)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) S tuples: MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(tl(incr(0))) -> c17(MARK(incr(0))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(tl(incr(s(z0)))) -> c17(MARK(incr(s(z0)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c16_1, c17_1, c16_2, c17_2, c8_1, c10_1, c13_1, c15_1 ---------------------------------------- (189) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing nodes: MARK(tl(incr(0))) -> c17(MARK(incr(0))) MARK(hd(incr(s(z0)))) -> c16(MARK(incr(s(z0)))) MARK(tl(incr(s(z0)))) -> c17(MARK(incr(s(z0)))) MARK(hd(incr(0))) -> c16(MARK(incr(0))) ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, 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A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) S tuples: MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats)), MARK(incr(nats))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros)), MARK(incr(zeros))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats)), MARK(incr(nats))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros)), MARK(incr(zeros))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1))), MARK(incr(cons(z0, z1)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c16_1, c17_1, c16_2, c17_2, c8_1, c10_1, c13_1, c15_1 ---------------------------------------- (191) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1)))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) S tuples: MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> 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A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) 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A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> 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MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1)))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c16_1, c17_1, c16_2, c17_2, c8_1, c10_1, c13_1, c15_1 ---------------------------------------- (193) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(a__incr(cons(z0, z1)))) by MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(cons(s(z0), incr(z1)))) MARK(hd(incr(cons(x0, x1)))) -> c16(A__HD(incr(cons(x0, x1)))) ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(cons(s(z0), incr(z1)))) MARK(hd(incr(cons(x0, x1)))) -> c16(A__HD(incr(cons(x0, x1)))) S tuples: MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(cons(s(z0), incr(z1)))) MARK(hd(incr(cons(x0, x1)))) -> c16(A__HD(incr(cons(x0, x1)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c16_1, c17_1, c16_2, c17_2, c8_1, c10_1, c13_1, c15_1 ---------------------------------------- (195) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(cons(s(z0), incr(z1)))) MARK(hd(incr(cons(x0, x1)))) -> c16(A__HD(incr(cons(x0, x1)))) ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> 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hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) S tuples: MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c16_1, c17_1, c16_2, c17_2, c8_1, c10_1, c13_1, c15_1 ---------------------------------------- (197) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(hd(cons(z0, z1))) -> c16(A__HD(cons(z0, z1))) by MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, 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c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) S tuples: MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c17_1, c16_2, c16_1, c17_2, c8_1, c10_1, c13_1, c15_1 ---------------------------------------- (199) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(tl(cons(z0, z1))) -> c17(A__TL(cons(z0, z1))) by MARK(tl(cons(z0, adx(y1)))) -> c17(A__TL(cons(z0, adx(y1)))) MARK(tl(cons(z0, incr(y1)))) -> c17(A__TL(cons(z0, incr(y1)))) MARK(tl(cons(z0, hd(cons(y1, y2))))) -> c17(A__TL(cons(z0, hd(cons(y1, y2))))) MARK(tl(cons(z0, tl(cons(y1, y2))))) -> c17(A__TL(cons(z0, tl(cons(y1, y2))))) MARK(tl(cons(z0, hd(adx(nats))))) -> c17(A__TL(cons(z0, hd(adx(nats))))) MARK(tl(cons(z0, hd(adx(adx(y1)))))) -> c17(A__TL(cons(z0, hd(adx(adx(y1)))))) MARK(tl(cons(z0, hd(adx(zeros))))) -> c17(A__TL(cons(z0, hd(adx(zeros))))) MARK(tl(cons(z0, hd(adx(incr(y1)))))) -> c17(A__TL(cons(z0, hd(adx(incr(y1)))))) MARK(tl(cons(z0, hd(adx(hd(y1)))))) -> c17(A__TL(cons(z0, hd(adx(hd(y1)))))) MARK(tl(cons(z0, hd(adx(tl(y1)))))) -> c17(A__TL(cons(z0, hd(adx(tl(y1)))))) MARK(tl(cons(z0, hd(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(adx(cons(y1, y2)))))) MARK(tl(cons(z0, hd(adx(y1))))) -> c17(A__TL(cons(z0, hd(adx(y1))))) MARK(tl(cons(z0, hd(incr(nats))))) -> c17(A__TL(cons(z0, hd(incr(nats))))) MARK(tl(cons(z0, hd(incr(adx(y1)))))) -> c17(A__TL(cons(z0, hd(incr(adx(y1)))))) MARK(tl(cons(z0, hd(incr(zeros))))) -> c17(A__TL(cons(z0, hd(incr(zeros))))) MARK(tl(cons(z0, hd(incr(incr(y1)))))) -> c17(A__TL(cons(z0, hd(incr(incr(y1)))))) MARK(tl(cons(z0, hd(incr(hd(y1)))))) -> c17(A__TL(cons(z0, hd(incr(hd(y1)))))) MARK(tl(cons(z0, hd(incr(tl(y1)))))) -> c17(A__TL(cons(z0, hd(incr(tl(y1)))))) MARK(tl(cons(z0, hd(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(incr(cons(y1, y2)))))) MARK(tl(cons(z0, hd(incr(y1))))) -> c17(A__TL(cons(z0, hd(incr(y1))))) MARK(tl(cons(z0, hd(hd(nats))))) -> c17(A__TL(cons(z0, hd(hd(nats))))) MARK(tl(cons(z0, hd(hd(adx(y1)))))) -> c17(A__TL(cons(z0, hd(hd(adx(y1)))))) MARK(tl(cons(z0, hd(hd(incr(y1)))))) -> c17(A__TL(cons(z0, hd(hd(incr(y1)))))) MARK(tl(cons(z0, hd(hd(hd(y1)))))) -> c17(A__TL(cons(z0, hd(hd(hd(y1)))))) MARK(tl(cons(z0, hd(hd(tl(y1)))))) -> c17(A__TL(cons(z0, hd(hd(tl(y1)))))) MARK(tl(cons(z0, hd(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(hd(cons(y1, y2)))))) MARK(tl(cons(z0, hd(hd(y1))))) -> c17(A__TL(cons(z0, hd(hd(y1))))) MARK(tl(cons(z0, hd(tl(nats))))) -> c17(A__TL(cons(z0, hd(tl(nats))))) MARK(tl(cons(z0, hd(tl(adx(y1)))))) -> c17(A__TL(cons(z0, hd(tl(adx(y1)))))) MARK(tl(cons(z0, hd(tl(zeros))))) -> c17(A__TL(cons(z0, hd(tl(zeros))))) MARK(tl(cons(z0, hd(tl(incr(y1)))))) -> c17(A__TL(cons(z0, hd(tl(incr(y1)))))) MARK(tl(cons(z0, hd(tl(hd(y1)))))) -> c17(A__TL(cons(z0, hd(tl(hd(y1)))))) MARK(tl(cons(z0, hd(tl(tl(y1)))))) -> c17(A__TL(cons(z0, hd(tl(tl(y1)))))) MARK(tl(cons(z0, hd(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(tl(cons(y1, y2)))))) MARK(tl(cons(z0, hd(tl(y1))))) -> c17(A__TL(cons(z0, hd(tl(y1))))) MARK(tl(cons(z0, hd(nats)))) -> c17(A__TL(cons(z0, hd(nats)))) MARK(tl(cons(z0, tl(adx(nats))))) -> c17(A__TL(cons(z0, tl(adx(nats))))) MARK(tl(cons(z0, tl(adx(adx(y1)))))) -> c17(A__TL(cons(z0, tl(adx(adx(y1)))))) MARK(tl(cons(z0, tl(adx(zeros))))) -> c17(A__TL(cons(z0, tl(adx(zeros))))) MARK(tl(cons(z0, tl(adx(incr(y1)))))) -> c17(A__TL(cons(z0, tl(adx(incr(y1)))))) MARK(tl(cons(z0, tl(adx(hd(y1)))))) -> c17(A__TL(cons(z0, tl(adx(hd(y1)))))) MARK(tl(cons(z0, tl(adx(tl(y1)))))) -> c17(A__TL(cons(z0, tl(adx(tl(y1)))))) MARK(tl(cons(z0, tl(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(adx(cons(y1, y2)))))) MARK(tl(cons(z0, tl(adx(s(y1)))))) -> c17(A__TL(cons(z0, tl(adx(s(y1)))))) MARK(tl(cons(z0, tl(adx(y1))))) -> c17(A__TL(cons(z0, tl(adx(y1))))) MARK(tl(cons(z0, tl(incr(nats))))) -> c17(A__TL(cons(z0, tl(incr(nats))))) MARK(tl(cons(z0, tl(incr(adx(y1)))))) -> c17(A__TL(cons(z0, tl(incr(adx(y1)))))) MARK(tl(cons(z0, tl(incr(zeros))))) -> c17(A__TL(cons(z0, tl(incr(zeros))))) MARK(tl(cons(z0, tl(incr(incr(y1)))))) -> c17(A__TL(cons(z0, tl(incr(incr(y1)))))) MARK(tl(cons(z0, tl(incr(hd(y1)))))) -> c17(A__TL(cons(z0, tl(incr(hd(y1)))))) MARK(tl(cons(z0, tl(incr(tl(y1)))))) -> c17(A__TL(cons(z0, tl(incr(tl(y1)))))) MARK(tl(cons(z0, tl(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(incr(cons(y1, y2)))))) MARK(tl(cons(z0, tl(incr(0))))) -> c17(A__TL(cons(z0, tl(incr(0))))) MARK(tl(cons(z0, tl(incr(s(y1)))))) -> c17(A__TL(cons(z0, tl(incr(s(y1)))))) MARK(tl(cons(z0, tl(incr(y1))))) -> c17(A__TL(cons(z0, tl(incr(y1))))) MARK(tl(cons(z0, tl(hd(nats))))) -> c17(A__TL(cons(z0, tl(hd(nats))))) MARK(tl(cons(z0, tl(hd(adx(y1)))))) -> c17(A__TL(cons(z0, tl(hd(adx(y1)))))) MARK(tl(cons(z0, tl(hd(incr(y1)))))) -> c17(A__TL(cons(z0, tl(hd(incr(y1)))))) MARK(tl(cons(z0, tl(hd(hd(y1)))))) -> c17(A__TL(cons(z0, tl(hd(hd(y1)))))) MARK(tl(cons(z0, tl(hd(tl(y1)))))) -> c17(A__TL(cons(z0, tl(hd(tl(y1)))))) MARK(tl(cons(z0, tl(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(hd(cons(y1, y2)))))) MARK(tl(cons(z0, tl(hd(y1))))) -> c17(A__TL(cons(z0, tl(hd(y1))))) MARK(tl(cons(z0, tl(tl(nats))))) -> c17(A__TL(cons(z0, tl(tl(nats))))) MARK(tl(cons(z0, tl(tl(adx(y1)))))) -> c17(A__TL(cons(z0, tl(tl(adx(y1)))))) MARK(tl(cons(z0, tl(tl(zeros))))) -> c17(A__TL(cons(z0, tl(tl(zeros))))) MARK(tl(cons(z0, tl(tl(incr(y1)))))) -> c17(A__TL(cons(z0, tl(tl(incr(y1)))))) MARK(tl(cons(z0, tl(tl(hd(y1)))))) -> c17(A__TL(cons(z0, tl(tl(hd(y1)))))) MARK(tl(cons(z0, tl(tl(tl(y1)))))) -> c17(A__TL(cons(z0, tl(tl(tl(y1)))))) MARK(tl(cons(z0, tl(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(tl(cons(y1, y2)))))) MARK(tl(cons(z0, tl(tl(y1))))) -> c17(A__TL(cons(z0, tl(tl(y1))))) MARK(tl(cons(z0, tl(nats)))) -> c17(A__TL(cons(z0, tl(nats)))) MARK(tl(cons(z0, hd(adx(0))))) -> c17(A__TL(cons(z0, hd(adx(0))))) MARK(tl(cons(z0, hd(adx(s(y1)))))) -> c17(A__TL(cons(z0, hd(adx(s(y1)))))) MARK(tl(cons(z0, hd(incr(0))))) -> c17(A__TL(cons(z0, hd(incr(0))))) MARK(tl(cons(z0, hd(incr(s(y1)))))) -> c17(A__TL(cons(z0, hd(incr(s(y1)))))) MARK(tl(cons(z0, hd(hd(zeros))))) -> c17(A__TL(cons(z0, hd(hd(zeros))))) MARK(tl(cons(z0, tl(hd(zeros))))) -> c17(A__TL(cons(z0, tl(hd(zeros))))) MARK(tl(cons(z0, tl(adx(0))))) -> c17(A__TL(cons(z0, tl(adx(0))))) ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), 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tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) MARK(tl(cons(z0, adx(y1)))) -> c17(A__TL(cons(z0, adx(y1)))) MARK(tl(cons(z0, incr(y1)))) -> c17(A__TL(cons(z0, incr(y1)))) MARK(tl(cons(z0, hd(cons(y1, y2))))) -> c17(A__TL(cons(z0, hd(cons(y1, y2))))) MARK(tl(cons(z0, tl(cons(y1, y2))))) -> c17(A__TL(cons(z0, tl(cons(y1, y2))))) MARK(tl(cons(z0, hd(adx(nats))))) -> c17(A__TL(cons(z0, hd(adx(nats))))) MARK(tl(cons(z0, hd(adx(adx(y1)))))) -> c17(A__TL(cons(z0, hd(adx(adx(y1)))))) MARK(tl(cons(z0, hd(adx(zeros))))) -> c17(A__TL(cons(z0, hd(adx(zeros))))) MARK(tl(cons(z0, hd(adx(incr(y1)))))) -> c17(A__TL(cons(z0, hd(adx(incr(y1)))))) MARK(tl(cons(z0, hd(adx(hd(y1)))))) -> c17(A__TL(cons(z0, hd(adx(hd(y1)))))) MARK(tl(cons(z0, hd(adx(tl(y1)))))) -> c17(A__TL(cons(z0, hd(adx(tl(y1)))))) MARK(tl(cons(z0, hd(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(adx(cons(y1, y2)))))) MARK(tl(cons(z0, hd(adx(y1))))) -> c17(A__TL(cons(z0, hd(adx(y1))))) MARK(tl(cons(z0, hd(incr(nats))))) -> c17(A__TL(cons(z0, hd(incr(nats))))) MARK(tl(cons(z0, hd(incr(adx(y1)))))) -> c17(A__TL(cons(z0, hd(incr(adx(y1)))))) MARK(tl(cons(z0, hd(incr(zeros))))) -> c17(A__TL(cons(z0, hd(incr(zeros))))) MARK(tl(cons(z0, hd(incr(incr(y1)))))) -> c17(A__TL(cons(z0, hd(incr(incr(y1)))))) MARK(tl(cons(z0, hd(incr(hd(y1)))))) -> c17(A__TL(cons(z0, hd(incr(hd(y1)))))) MARK(tl(cons(z0, hd(incr(tl(y1)))))) -> c17(A__TL(cons(z0, hd(incr(tl(y1)))))) MARK(tl(cons(z0, hd(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(incr(cons(y1, y2)))))) MARK(tl(cons(z0, hd(incr(y1))))) -> c17(A__TL(cons(z0, hd(incr(y1))))) MARK(tl(cons(z0, hd(hd(nats))))) -> c17(A__TL(cons(z0, hd(hd(nats))))) MARK(tl(cons(z0, hd(hd(adx(y1)))))) -> c17(A__TL(cons(z0, hd(hd(adx(y1)))))) MARK(tl(cons(z0, hd(hd(incr(y1)))))) -> c17(A__TL(cons(z0, hd(hd(incr(y1)))))) MARK(tl(cons(z0, hd(hd(hd(y1)))))) -> c17(A__TL(cons(z0, hd(hd(hd(y1)))))) MARK(tl(cons(z0, hd(hd(tl(y1)))))) -> c17(A__TL(cons(z0, hd(hd(tl(y1)))))) MARK(tl(cons(z0, hd(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(hd(cons(y1, y2)))))) MARK(tl(cons(z0, hd(hd(y1))))) -> c17(A__TL(cons(z0, hd(hd(y1))))) MARK(tl(cons(z0, hd(tl(nats))))) -> c17(A__TL(cons(z0, hd(tl(nats))))) MARK(tl(cons(z0, hd(tl(adx(y1)))))) -> c17(A__TL(cons(z0, hd(tl(adx(y1)))))) MARK(tl(cons(z0, hd(tl(zeros))))) -> c17(A__TL(cons(z0, hd(tl(zeros))))) MARK(tl(cons(z0, hd(tl(incr(y1)))))) -> c17(A__TL(cons(z0, hd(tl(incr(y1)))))) MARK(tl(cons(z0, hd(tl(hd(y1)))))) -> c17(A__TL(cons(z0, hd(tl(hd(y1)))))) MARK(tl(cons(z0, hd(tl(tl(y1)))))) -> c17(A__TL(cons(z0, hd(tl(tl(y1)))))) MARK(tl(cons(z0, hd(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(tl(cons(y1, y2)))))) MARK(tl(cons(z0, hd(tl(y1))))) -> c17(A__TL(cons(z0, hd(tl(y1))))) MARK(tl(cons(z0, hd(nats)))) -> c17(A__TL(cons(z0, hd(nats)))) MARK(tl(cons(z0, tl(adx(nats))))) -> c17(A__TL(cons(z0, tl(adx(nats))))) MARK(tl(cons(z0, tl(adx(adx(y1)))))) -> c17(A__TL(cons(z0, tl(adx(adx(y1)))))) MARK(tl(cons(z0, tl(adx(zeros))))) -> c17(A__TL(cons(z0, tl(adx(zeros))))) MARK(tl(cons(z0, tl(adx(incr(y1)))))) -> c17(A__TL(cons(z0, tl(adx(incr(y1)))))) MARK(tl(cons(z0, tl(adx(hd(y1)))))) -> c17(A__TL(cons(z0, tl(adx(hd(y1)))))) MARK(tl(cons(z0, tl(adx(tl(y1)))))) -> c17(A__TL(cons(z0, tl(adx(tl(y1)))))) MARK(tl(cons(z0, tl(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(adx(cons(y1, y2)))))) MARK(tl(cons(z0, tl(adx(s(y1)))))) -> c17(A__TL(cons(z0, tl(adx(s(y1)))))) MARK(tl(cons(z0, tl(adx(y1))))) -> c17(A__TL(cons(z0, tl(adx(y1))))) MARK(tl(cons(z0, tl(incr(nats))))) -> c17(A__TL(cons(z0, tl(incr(nats))))) MARK(tl(cons(z0, tl(incr(adx(y1)))))) -> c17(A__TL(cons(z0, tl(incr(adx(y1)))))) MARK(tl(cons(z0, tl(incr(zeros))))) -> c17(A__TL(cons(z0, tl(incr(zeros))))) MARK(tl(cons(z0, tl(incr(incr(y1)))))) -> c17(A__TL(cons(z0, tl(incr(incr(y1)))))) MARK(tl(cons(z0, tl(incr(hd(y1)))))) -> c17(A__TL(cons(z0, tl(incr(hd(y1)))))) MARK(tl(cons(z0, tl(incr(tl(y1)))))) -> c17(A__TL(cons(z0, tl(incr(tl(y1)))))) MARK(tl(cons(z0, tl(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(incr(cons(y1, y2)))))) MARK(tl(cons(z0, tl(incr(0))))) -> c17(A__TL(cons(z0, tl(incr(0))))) MARK(tl(cons(z0, tl(incr(s(y1)))))) -> c17(A__TL(cons(z0, tl(incr(s(y1)))))) MARK(tl(cons(z0, tl(incr(y1))))) -> c17(A__TL(cons(z0, tl(incr(y1))))) MARK(tl(cons(z0, tl(hd(nats))))) -> c17(A__TL(cons(z0, tl(hd(nats))))) MARK(tl(cons(z0, tl(hd(adx(y1)))))) -> c17(A__TL(cons(z0, tl(hd(adx(y1)))))) MARK(tl(cons(z0, tl(hd(incr(y1)))))) -> c17(A__TL(cons(z0, tl(hd(incr(y1)))))) MARK(tl(cons(z0, tl(hd(hd(y1)))))) -> c17(A__TL(cons(z0, tl(hd(hd(y1)))))) MARK(tl(cons(z0, tl(hd(tl(y1)))))) -> c17(A__TL(cons(z0, tl(hd(tl(y1)))))) MARK(tl(cons(z0, tl(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(hd(cons(y1, y2)))))) MARK(tl(cons(z0, tl(hd(y1))))) -> c17(A__TL(cons(z0, tl(hd(y1))))) MARK(tl(cons(z0, tl(tl(nats))))) -> c17(A__TL(cons(z0, tl(tl(nats))))) MARK(tl(cons(z0, tl(tl(adx(y1)))))) -> c17(A__TL(cons(z0, tl(tl(adx(y1)))))) MARK(tl(cons(z0, tl(tl(zeros))))) -> c17(A__TL(cons(z0, tl(tl(zeros))))) MARK(tl(cons(z0, tl(tl(incr(y1)))))) -> c17(A__TL(cons(z0, tl(tl(incr(y1)))))) MARK(tl(cons(z0, tl(tl(hd(y1)))))) -> c17(A__TL(cons(z0, tl(tl(hd(y1)))))) MARK(tl(cons(z0, tl(tl(tl(y1)))))) -> c17(A__TL(cons(z0, tl(tl(tl(y1)))))) MARK(tl(cons(z0, tl(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(tl(cons(y1, y2)))))) MARK(tl(cons(z0, tl(tl(y1))))) -> c17(A__TL(cons(z0, tl(tl(y1))))) MARK(tl(cons(z0, tl(nats)))) -> c17(A__TL(cons(z0, tl(nats)))) MARK(tl(cons(z0, hd(adx(0))))) -> c17(A__TL(cons(z0, hd(adx(0))))) MARK(tl(cons(z0, hd(adx(s(y1)))))) -> c17(A__TL(cons(z0, hd(adx(s(y1)))))) MARK(tl(cons(z0, hd(incr(0))))) -> c17(A__TL(cons(z0, hd(incr(0))))) MARK(tl(cons(z0, hd(incr(s(y1)))))) -> c17(A__TL(cons(z0, hd(incr(s(y1)))))) MARK(tl(cons(z0, hd(hd(zeros))))) -> c17(A__TL(cons(z0, hd(hd(zeros))))) MARK(tl(cons(z0, tl(hd(zeros))))) -> c17(A__TL(cons(z0, tl(hd(zeros))))) MARK(tl(cons(z0, tl(adx(0))))) -> c17(A__TL(cons(z0, tl(adx(0))))) S tuples: MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) MARK(tl(cons(z0, adx(y1)))) -> c17(A__TL(cons(z0, adx(y1)))) MARK(tl(cons(z0, incr(y1)))) -> c17(A__TL(cons(z0, incr(y1)))) MARK(tl(cons(z0, hd(cons(y1, y2))))) -> c17(A__TL(cons(z0, hd(cons(y1, y2))))) MARK(tl(cons(z0, tl(cons(y1, y2))))) -> c17(A__TL(cons(z0, tl(cons(y1, y2))))) MARK(tl(cons(z0, hd(adx(nats))))) -> c17(A__TL(cons(z0, hd(adx(nats))))) MARK(tl(cons(z0, hd(adx(adx(y1)))))) -> c17(A__TL(cons(z0, hd(adx(adx(y1)))))) MARK(tl(cons(z0, hd(adx(zeros))))) -> c17(A__TL(cons(z0, hd(adx(zeros))))) MARK(tl(cons(z0, hd(adx(incr(y1)))))) -> c17(A__TL(cons(z0, hd(adx(incr(y1)))))) MARK(tl(cons(z0, hd(adx(hd(y1)))))) -> c17(A__TL(cons(z0, hd(adx(hd(y1)))))) MARK(tl(cons(z0, hd(adx(tl(y1)))))) -> c17(A__TL(cons(z0, hd(adx(tl(y1)))))) MARK(tl(cons(z0, hd(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(adx(cons(y1, y2)))))) MARK(tl(cons(z0, hd(adx(y1))))) -> c17(A__TL(cons(z0, hd(adx(y1))))) MARK(tl(cons(z0, hd(incr(nats))))) -> c17(A__TL(cons(z0, hd(incr(nats))))) MARK(tl(cons(z0, hd(incr(adx(y1)))))) -> c17(A__TL(cons(z0, hd(incr(adx(y1)))))) MARK(tl(cons(z0, hd(incr(zeros))))) -> c17(A__TL(cons(z0, hd(incr(zeros))))) MARK(tl(cons(z0, hd(incr(incr(y1)))))) -> c17(A__TL(cons(z0, hd(incr(incr(y1)))))) MARK(tl(cons(z0, hd(incr(hd(y1)))))) -> c17(A__TL(cons(z0, hd(incr(hd(y1)))))) MARK(tl(cons(z0, hd(incr(tl(y1)))))) -> c17(A__TL(cons(z0, hd(incr(tl(y1)))))) MARK(tl(cons(z0, hd(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(incr(cons(y1, y2)))))) MARK(tl(cons(z0, hd(incr(y1))))) -> c17(A__TL(cons(z0, hd(incr(y1))))) MARK(tl(cons(z0, hd(hd(nats))))) -> c17(A__TL(cons(z0, hd(hd(nats))))) MARK(tl(cons(z0, hd(hd(adx(y1)))))) -> c17(A__TL(cons(z0, hd(hd(adx(y1)))))) MARK(tl(cons(z0, hd(hd(incr(y1)))))) -> c17(A__TL(cons(z0, hd(hd(incr(y1)))))) MARK(tl(cons(z0, hd(hd(hd(y1)))))) -> c17(A__TL(cons(z0, hd(hd(hd(y1)))))) MARK(tl(cons(z0, hd(hd(tl(y1)))))) -> c17(A__TL(cons(z0, hd(hd(tl(y1)))))) MARK(tl(cons(z0, hd(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(hd(cons(y1, y2)))))) MARK(tl(cons(z0, hd(hd(y1))))) -> c17(A__TL(cons(z0, hd(hd(y1))))) MARK(tl(cons(z0, hd(tl(nats))))) -> c17(A__TL(cons(z0, hd(tl(nats))))) MARK(tl(cons(z0, hd(tl(adx(y1)))))) -> c17(A__TL(cons(z0, hd(tl(adx(y1)))))) MARK(tl(cons(z0, hd(tl(zeros))))) -> c17(A__TL(cons(z0, hd(tl(zeros))))) MARK(tl(cons(z0, hd(tl(incr(y1)))))) -> c17(A__TL(cons(z0, hd(tl(incr(y1)))))) MARK(tl(cons(z0, hd(tl(hd(y1)))))) -> c17(A__TL(cons(z0, hd(tl(hd(y1)))))) MARK(tl(cons(z0, hd(tl(tl(y1)))))) -> c17(A__TL(cons(z0, hd(tl(tl(y1)))))) MARK(tl(cons(z0, hd(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(tl(cons(y1, y2)))))) MARK(tl(cons(z0, hd(tl(y1))))) -> c17(A__TL(cons(z0, hd(tl(y1))))) MARK(tl(cons(z0, hd(nats)))) -> c17(A__TL(cons(z0, hd(nats)))) MARK(tl(cons(z0, tl(adx(nats))))) -> c17(A__TL(cons(z0, tl(adx(nats))))) MARK(tl(cons(z0, tl(adx(adx(y1)))))) -> c17(A__TL(cons(z0, tl(adx(adx(y1)))))) MARK(tl(cons(z0, tl(adx(zeros))))) -> c17(A__TL(cons(z0, tl(adx(zeros))))) MARK(tl(cons(z0, tl(adx(incr(y1)))))) -> c17(A__TL(cons(z0, tl(adx(incr(y1)))))) MARK(tl(cons(z0, tl(adx(hd(y1)))))) -> c17(A__TL(cons(z0, tl(adx(hd(y1)))))) MARK(tl(cons(z0, tl(adx(tl(y1)))))) -> c17(A__TL(cons(z0, tl(adx(tl(y1)))))) MARK(tl(cons(z0, tl(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(adx(cons(y1, y2)))))) MARK(tl(cons(z0, tl(adx(s(y1)))))) -> c17(A__TL(cons(z0, tl(adx(s(y1)))))) MARK(tl(cons(z0, tl(adx(y1))))) -> c17(A__TL(cons(z0, tl(adx(y1))))) MARK(tl(cons(z0, tl(incr(nats))))) -> c17(A__TL(cons(z0, tl(incr(nats))))) MARK(tl(cons(z0, tl(incr(adx(y1)))))) -> c17(A__TL(cons(z0, tl(incr(adx(y1)))))) MARK(tl(cons(z0, tl(incr(zeros))))) -> c17(A__TL(cons(z0, tl(incr(zeros))))) MARK(tl(cons(z0, tl(incr(incr(y1)))))) -> c17(A__TL(cons(z0, tl(incr(incr(y1)))))) MARK(tl(cons(z0, tl(incr(hd(y1)))))) -> c17(A__TL(cons(z0, tl(incr(hd(y1)))))) MARK(tl(cons(z0, tl(incr(tl(y1)))))) -> c17(A__TL(cons(z0, tl(incr(tl(y1)))))) MARK(tl(cons(z0, tl(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(incr(cons(y1, y2)))))) MARK(tl(cons(z0, tl(incr(0))))) -> c17(A__TL(cons(z0, tl(incr(0))))) MARK(tl(cons(z0, tl(incr(s(y1)))))) -> c17(A__TL(cons(z0, tl(incr(s(y1)))))) MARK(tl(cons(z0, tl(incr(y1))))) -> c17(A__TL(cons(z0, tl(incr(y1))))) MARK(tl(cons(z0, tl(hd(nats))))) -> c17(A__TL(cons(z0, tl(hd(nats))))) MARK(tl(cons(z0, tl(hd(adx(y1)))))) -> c17(A__TL(cons(z0, tl(hd(adx(y1)))))) MARK(tl(cons(z0, tl(hd(incr(y1)))))) -> c17(A__TL(cons(z0, tl(hd(incr(y1)))))) MARK(tl(cons(z0, tl(hd(hd(y1)))))) -> c17(A__TL(cons(z0, tl(hd(hd(y1)))))) MARK(tl(cons(z0, tl(hd(tl(y1)))))) -> c17(A__TL(cons(z0, tl(hd(tl(y1)))))) MARK(tl(cons(z0, tl(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(hd(cons(y1, y2)))))) MARK(tl(cons(z0, tl(hd(y1))))) -> c17(A__TL(cons(z0, tl(hd(y1))))) MARK(tl(cons(z0, tl(tl(nats))))) -> c17(A__TL(cons(z0, tl(tl(nats))))) MARK(tl(cons(z0, tl(tl(adx(y1)))))) -> c17(A__TL(cons(z0, tl(tl(adx(y1)))))) MARK(tl(cons(z0, tl(tl(zeros))))) -> c17(A__TL(cons(z0, tl(tl(zeros))))) MARK(tl(cons(z0, tl(tl(incr(y1)))))) -> c17(A__TL(cons(z0, tl(tl(incr(y1)))))) MARK(tl(cons(z0, tl(tl(hd(y1)))))) -> c17(A__TL(cons(z0, tl(tl(hd(y1)))))) MARK(tl(cons(z0, tl(tl(tl(y1)))))) -> c17(A__TL(cons(z0, tl(tl(tl(y1)))))) MARK(tl(cons(z0, tl(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(tl(cons(y1, y2)))))) MARK(tl(cons(z0, tl(tl(y1))))) -> c17(A__TL(cons(z0, tl(tl(y1))))) MARK(tl(cons(z0, tl(nats)))) -> c17(A__TL(cons(z0, tl(nats)))) MARK(tl(cons(z0, hd(adx(0))))) -> c17(A__TL(cons(z0, hd(adx(0))))) MARK(tl(cons(z0, hd(adx(s(y1)))))) -> c17(A__TL(cons(z0, hd(adx(s(y1)))))) MARK(tl(cons(z0, hd(incr(0))))) -> c17(A__TL(cons(z0, hd(incr(0))))) MARK(tl(cons(z0, hd(incr(s(y1)))))) -> c17(A__TL(cons(z0, hd(incr(s(y1)))))) MARK(tl(cons(z0, hd(hd(zeros))))) -> c17(A__TL(cons(z0, hd(hd(zeros))))) MARK(tl(cons(z0, tl(hd(zeros))))) -> c17(A__TL(cons(z0, tl(hd(zeros))))) MARK(tl(cons(z0, tl(adx(0))))) -> c17(A__TL(cons(z0, tl(adx(0))))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c16_2, c16_1, c17_2, c17_1, c8_1, c10_1, c13_1, c15_1 ---------------------------------------- (201) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) by MARK(hd(adx(adx(y0)))) -> c16(MARK(adx(adx(y0)))) MARK(hd(adx(incr(y0)))) -> c16(MARK(adx(incr(y0)))) MARK(hd(adx(hd(cons(y0, y1))))) -> c16(MARK(adx(hd(cons(y0, y1))))) MARK(hd(adx(tl(cons(y0, y1))))) -> c16(MARK(adx(tl(cons(y0, y1))))) MARK(hd(adx(hd(adx(nats))))) -> c16(MARK(adx(hd(adx(nats))))) MARK(hd(adx(hd(adx(adx(y0)))))) -> c16(MARK(adx(hd(adx(adx(y0)))))) MARK(hd(adx(hd(adx(zeros))))) -> c16(MARK(adx(hd(adx(zeros))))) MARK(hd(adx(hd(adx(incr(y0)))))) -> c16(MARK(adx(hd(adx(incr(y0)))))) MARK(hd(adx(hd(adx(hd(y0)))))) -> c16(MARK(adx(hd(adx(hd(y0)))))) MARK(hd(adx(hd(adx(tl(y0)))))) -> c16(MARK(adx(hd(adx(tl(y0)))))) MARK(hd(adx(hd(adx(cons(y0, y1)))))) -> c16(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(hd(adx(hd(adx(y0))))) -> c16(MARK(adx(hd(adx(y0))))) MARK(hd(adx(hd(incr(nats))))) -> c16(MARK(adx(hd(incr(nats))))) MARK(hd(adx(hd(incr(adx(y0)))))) -> c16(MARK(adx(hd(incr(adx(y0)))))) MARK(hd(adx(hd(incr(zeros))))) -> c16(MARK(adx(hd(incr(zeros))))) MARK(hd(adx(hd(incr(incr(y0)))))) -> c16(MARK(adx(hd(incr(incr(y0)))))) MARK(hd(adx(hd(incr(hd(y0)))))) -> c16(MARK(adx(hd(incr(hd(y0)))))) MARK(hd(adx(hd(incr(tl(y0)))))) -> c16(MARK(adx(hd(incr(tl(y0)))))) MARK(hd(adx(hd(incr(cons(y0, y1)))))) -> c16(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(hd(adx(hd(incr(y0))))) -> c16(MARK(adx(hd(incr(y0))))) MARK(hd(adx(hd(hd(nats))))) -> c16(MARK(adx(hd(hd(nats))))) MARK(hd(adx(hd(hd(adx(y0)))))) -> c16(MARK(adx(hd(hd(adx(y0)))))) MARK(hd(adx(hd(hd(incr(y0)))))) -> c16(MARK(adx(hd(hd(incr(y0)))))) MARK(hd(adx(hd(hd(hd(y0)))))) -> c16(MARK(adx(hd(hd(hd(y0)))))) MARK(hd(adx(hd(hd(tl(y0)))))) -> c16(MARK(adx(hd(hd(tl(y0)))))) MARK(hd(adx(hd(hd(cons(y0, y1)))))) -> c16(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(hd(adx(hd(hd(y0))))) -> c16(MARK(adx(hd(hd(y0))))) MARK(hd(adx(hd(tl(nats))))) -> c16(MARK(adx(hd(tl(nats))))) MARK(hd(adx(hd(tl(adx(y0)))))) -> c16(MARK(adx(hd(tl(adx(y0)))))) MARK(hd(adx(hd(tl(incr(y0)))))) -> c16(MARK(adx(hd(tl(incr(y0)))))) MARK(hd(adx(hd(tl(hd(y0)))))) -> c16(MARK(adx(hd(tl(hd(y0)))))) MARK(hd(adx(hd(tl(tl(y0)))))) -> c16(MARK(adx(hd(tl(tl(y0)))))) MARK(hd(adx(hd(tl(cons(y0, y1)))))) -> c16(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(hd(adx(hd(tl(y0))))) -> c16(MARK(adx(hd(tl(y0))))) MARK(hd(adx(hd(nats)))) -> c16(MARK(adx(hd(nats)))) MARK(hd(adx(tl(adx(nats))))) -> c16(MARK(adx(tl(adx(nats))))) MARK(hd(adx(tl(adx(adx(y0)))))) -> c16(MARK(adx(tl(adx(adx(y0)))))) MARK(hd(adx(tl(adx(zeros))))) -> c16(MARK(adx(tl(adx(zeros))))) MARK(hd(adx(tl(adx(incr(y0)))))) -> c16(MARK(adx(tl(adx(incr(y0)))))) MARK(hd(adx(tl(adx(hd(y0)))))) -> c16(MARK(adx(tl(adx(hd(y0)))))) MARK(hd(adx(tl(adx(tl(y0)))))) -> c16(MARK(adx(tl(adx(tl(y0)))))) MARK(hd(adx(tl(adx(cons(y0, y1)))))) -> c16(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(hd(adx(tl(adx(y0))))) -> c16(MARK(adx(tl(adx(y0))))) MARK(hd(adx(tl(incr(nats))))) -> c16(MARK(adx(tl(incr(nats))))) MARK(hd(adx(tl(incr(adx(y0)))))) -> c16(MARK(adx(tl(incr(adx(y0)))))) MARK(hd(adx(tl(incr(zeros))))) -> c16(MARK(adx(tl(incr(zeros))))) MARK(hd(adx(tl(incr(incr(y0)))))) -> c16(MARK(adx(tl(incr(incr(y0)))))) MARK(hd(adx(tl(incr(hd(y0)))))) -> c16(MARK(adx(tl(incr(hd(y0)))))) MARK(hd(adx(tl(incr(tl(y0)))))) -> c16(MARK(adx(tl(incr(tl(y0)))))) MARK(hd(adx(tl(incr(cons(y0, y1)))))) -> c16(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(hd(adx(tl(incr(s(y0)))))) -> c16(MARK(adx(tl(incr(s(y0)))))) MARK(hd(adx(tl(incr(y0))))) -> c16(MARK(adx(tl(incr(y0))))) MARK(hd(adx(tl(hd(nats))))) -> c16(MARK(adx(tl(hd(nats))))) MARK(hd(adx(tl(hd(adx(y0)))))) -> c16(MARK(adx(tl(hd(adx(y0)))))) MARK(hd(adx(tl(hd(incr(y0)))))) -> c16(MARK(adx(tl(hd(incr(y0)))))) MARK(hd(adx(tl(hd(hd(y0)))))) -> c16(MARK(adx(tl(hd(hd(y0)))))) MARK(hd(adx(tl(hd(tl(y0)))))) -> c16(MARK(adx(tl(hd(tl(y0)))))) MARK(hd(adx(tl(hd(cons(y0, y1)))))) -> c16(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(hd(adx(tl(hd(y0))))) -> c16(MARK(adx(tl(hd(y0))))) MARK(hd(adx(tl(tl(nats))))) -> c16(MARK(adx(tl(tl(nats))))) MARK(hd(adx(tl(tl(adx(y0)))))) -> c16(MARK(adx(tl(tl(adx(y0)))))) MARK(hd(adx(tl(tl(incr(y0)))))) -> c16(MARK(adx(tl(tl(incr(y0)))))) MARK(hd(adx(tl(tl(hd(y0)))))) -> c16(MARK(adx(tl(tl(hd(y0)))))) MARK(hd(adx(tl(tl(tl(y0)))))) -> c16(MARK(adx(tl(tl(tl(y0)))))) MARK(hd(adx(tl(tl(cons(y0, y1)))))) -> c16(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(hd(adx(tl(tl(y0))))) -> c16(MARK(adx(tl(tl(y0))))) MARK(hd(adx(tl(nats)))) -> c16(MARK(adx(tl(nats)))) MARK(hd(adx(hd(adx(0))))) -> c16(MARK(adx(hd(adx(0))))) MARK(hd(adx(hd(adx(s(y0)))))) -> c16(MARK(adx(hd(adx(s(y0)))))) MARK(hd(adx(hd(incr(0))))) -> c16(MARK(adx(hd(incr(0))))) MARK(hd(adx(hd(incr(s(y0)))))) -> c16(MARK(adx(hd(incr(s(y0)))))) MARK(hd(adx(hd(hd(zeros))))) -> c16(MARK(adx(hd(hd(zeros))))) MARK(hd(adx(tl(hd(zeros))))) -> c16(MARK(adx(tl(hd(zeros))))) MARK(hd(adx(tl(adx(0))))) -> c16(MARK(adx(tl(adx(0))))) MARK(hd(adx(hd(tl(zeros))))) -> c16(MARK(adx(hd(tl(zeros))))) MARK(hd(adx(tl(tl(zeros))))) -> c16(MARK(adx(tl(tl(zeros))))) MARK(hd(adx(tl(adx(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) MARK(hd(adx(tl(incr(0))))) -> c16(MARK(adx(tl(incr(0))))) ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) MARK(tl(cons(z0, adx(y1)))) -> c17(A__TL(cons(z0, adx(y1)))) MARK(tl(cons(z0, incr(y1)))) -> c17(A__TL(cons(z0, incr(y1)))) MARK(tl(cons(z0, hd(cons(y1, y2))))) -> c17(A__TL(cons(z0, hd(cons(y1, y2))))) MARK(tl(cons(z0, tl(cons(y1, y2))))) -> c17(A__TL(cons(z0, tl(cons(y1, y2))))) MARK(tl(cons(z0, hd(adx(nats))))) -> c17(A__TL(cons(z0, hd(adx(nats))))) MARK(tl(cons(z0, hd(adx(adx(y1)))))) -> c17(A__TL(cons(z0, hd(adx(adx(y1)))))) MARK(tl(cons(z0, hd(adx(zeros))))) -> c17(A__TL(cons(z0, hd(adx(zeros))))) MARK(tl(cons(z0, hd(adx(incr(y1)))))) -> c17(A__TL(cons(z0, hd(adx(incr(y1)))))) MARK(tl(cons(z0, hd(adx(hd(y1)))))) -> c17(A__TL(cons(z0, hd(adx(hd(y1)))))) MARK(tl(cons(z0, hd(adx(tl(y1)))))) -> c17(A__TL(cons(z0, hd(adx(tl(y1)))))) MARK(tl(cons(z0, hd(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(adx(cons(y1, y2)))))) MARK(tl(cons(z0, hd(adx(y1))))) -> c17(A__TL(cons(z0, hd(adx(y1))))) MARK(tl(cons(z0, hd(incr(nats))))) -> c17(A__TL(cons(z0, hd(incr(nats))))) MARK(tl(cons(z0, hd(incr(adx(y1)))))) -> c17(A__TL(cons(z0, hd(incr(adx(y1)))))) MARK(tl(cons(z0, hd(incr(zeros))))) -> c17(A__TL(cons(z0, hd(incr(zeros))))) MARK(tl(cons(z0, hd(incr(incr(y1)))))) -> c17(A__TL(cons(z0, hd(incr(incr(y1)))))) MARK(tl(cons(z0, hd(incr(hd(y1)))))) -> c17(A__TL(cons(z0, hd(incr(hd(y1)))))) MARK(tl(cons(z0, hd(incr(tl(y1)))))) -> c17(A__TL(cons(z0, hd(incr(tl(y1)))))) MARK(tl(cons(z0, hd(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(incr(cons(y1, y2)))))) MARK(tl(cons(z0, hd(incr(y1))))) -> c17(A__TL(cons(z0, hd(incr(y1))))) MARK(tl(cons(z0, hd(hd(nats))))) -> c17(A__TL(cons(z0, hd(hd(nats))))) MARK(tl(cons(z0, hd(hd(adx(y1)))))) -> c17(A__TL(cons(z0, hd(hd(adx(y1)))))) MARK(tl(cons(z0, hd(hd(incr(y1)))))) -> c17(A__TL(cons(z0, hd(hd(incr(y1)))))) MARK(tl(cons(z0, hd(hd(hd(y1)))))) -> c17(A__TL(cons(z0, hd(hd(hd(y1)))))) MARK(tl(cons(z0, hd(hd(tl(y1)))))) -> c17(A__TL(cons(z0, hd(hd(tl(y1)))))) MARK(tl(cons(z0, hd(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(hd(cons(y1, y2)))))) MARK(tl(cons(z0, hd(hd(y1))))) -> c17(A__TL(cons(z0, hd(hd(y1))))) MARK(tl(cons(z0, hd(tl(nats))))) -> c17(A__TL(cons(z0, hd(tl(nats))))) MARK(tl(cons(z0, hd(tl(adx(y1)))))) -> c17(A__TL(cons(z0, hd(tl(adx(y1)))))) MARK(tl(cons(z0, hd(tl(zeros))))) -> c17(A__TL(cons(z0, hd(tl(zeros))))) MARK(tl(cons(z0, hd(tl(incr(y1)))))) -> c17(A__TL(cons(z0, hd(tl(incr(y1)))))) MARK(tl(cons(z0, hd(tl(hd(y1)))))) -> c17(A__TL(cons(z0, hd(tl(hd(y1)))))) MARK(tl(cons(z0, hd(tl(tl(y1)))))) -> c17(A__TL(cons(z0, hd(tl(tl(y1)))))) MARK(tl(cons(z0, hd(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(tl(cons(y1, y2)))))) MARK(tl(cons(z0, hd(tl(y1))))) -> c17(A__TL(cons(z0, hd(tl(y1))))) MARK(tl(cons(z0, hd(nats)))) -> c17(A__TL(cons(z0, hd(nats)))) MARK(tl(cons(z0, tl(adx(nats))))) -> c17(A__TL(cons(z0, tl(adx(nats))))) MARK(tl(cons(z0, tl(adx(adx(y1)))))) -> c17(A__TL(cons(z0, tl(adx(adx(y1)))))) MARK(tl(cons(z0, tl(adx(zeros))))) -> c17(A__TL(cons(z0, tl(adx(zeros))))) MARK(tl(cons(z0, tl(adx(incr(y1)))))) -> c17(A__TL(cons(z0, tl(adx(incr(y1)))))) MARK(tl(cons(z0, tl(adx(hd(y1)))))) -> c17(A__TL(cons(z0, tl(adx(hd(y1)))))) MARK(tl(cons(z0, tl(adx(tl(y1)))))) -> c17(A__TL(cons(z0, tl(adx(tl(y1)))))) MARK(tl(cons(z0, tl(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(adx(cons(y1, y2)))))) MARK(tl(cons(z0, tl(adx(s(y1)))))) -> c17(A__TL(cons(z0, tl(adx(s(y1)))))) MARK(tl(cons(z0, tl(adx(y1))))) -> c17(A__TL(cons(z0, tl(adx(y1))))) MARK(tl(cons(z0, tl(incr(nats))))) -> c17(A__TL(cons(z0, tl(incr(nats))))) MARK(tl(cons(z0, tl(incr(adx(y1)))))) -> c17(A__TL(cons(z0, tl(incr(adx(y1)))))) MARK(tl(cons(z0, tl(incr(zeros))))) -> c17(A__TL(cons(z0, tl(incr(zeros))))) MARK(tl(cons(z0, tl(incr(incr(y1)))))) -> c17(A__TL(cons(z0, tl(incr(incr(y1)))))) MARK(tl(cons(z0, tl(incr(hd(y1)))))) -> c17(A__TL(cons(z0, tl(incr(hd(y1)))))) MARK(tl(cons(z0, tl(incr(tl(y1)))))) -> c17(A__TL(cons(z0, tl(incr(tl(y1)))))) MARK(tl(cons(z0, tl(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(incr(cons(y1, y2)))))) MARK(tl(cons(z0, tl(incr(0))))) -> c17(A__TL(cons(z0, tl(incr(0))))) MARK(tl(cons(z0, tl(incr(s(y1)))))) -> c17(A__TL(cons(z0, tl(incr(s(y1)))))) MARK(tl(cons(z0, tl(incr(y1))))) -> c17(A__TL(cons(z0, tl(incr(y1))))) MARK(tl(cons(z0, tl(hd(nats))))) -> c17(A__TL(cons(z0, tl(hd(nats))))) MARK(tl(cons(z0, tl(hd(adx(y1)))))) -> c17(A__TL(cons(z0, tl(hd(adx(y1)))))) MARK(tl(cons(z0, tl(hd(incr(y1)))))) -> c17(A__TL(cons(z0, tl(hd(incr(y1)))))) MARK(tl(cons(z0, tl(hd(hd(y1)))))) -> c17(A__TL(cons(z0, tl(hd(hd(y1)))))) MARK(tl(cons(z0, tl(hd(tl(y1)))))) -> c17(A__TL(cons(z0, tl(hd(tl(y1)))))) MARK(tl(cons(z0, tl(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(hd(cons(y1, y2)))))) MARK(tl(cons(z0, tl(hd(y1))))) -> c17(A__TL(cons(z0, tl(hd(y1))))) MARK(tl(cons(z0, tl(tl(nats))))) -> c17(A__TL(cons(z0, tl(tl(nats))))) MARK(tl(cons(z0, tl(tl(adx(y1)))))) -> c17(A__TL(cons(z0, tl(tl(adx(y1)))))) MARK(tl(cons(z0, tl(tl(zeros))))) -> c17(A__TL(cons(z0, tl(tl(zeros))))) MARK(tl(cons(z0, tl(tl(incr(y1)))))) -> c17(A__TL(cons(z0, tl(tl(incr(y1)))))) MARK(tl(cons(z0, tl(tl(hd(y1)))))) -> c17(A__TL(cons(z0, tl(tl(hd(y1)))))) MARK(tl(cons(z0, tl(tl(tl(y1)))))) -> c17(A__TL(cons(z0, tl(tl(tl(y1)))))) MARK(tl(cons(z0, tl(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(tl(cons(y1, y2)))))) MARK(tl(cons(z0, tl(tl(y1))))) -> c17(A__TL(cons(z0, tl(tl(y1))))) MARK(tl(cons(z0, tl(nats)))) -> c17(A__TL(cons(z0, tl(nats)))) MARK(tl(cons(z0, hd(adx(0))))) -> c17(A__TL(cons(z0, hd(adx(0))))) MARK(tl(cons(z0, hd(adx(s(y1)))))) -> c17(A__TL(cons(z0, hd(adx(s(y1)))))) MARK(tl(cons(z0, hd(incr(0))))) -> c17(A__TL(cons(z0, hd(incr(0))))) MARK(tl(cons(z0, hd(incr(s(y1)))))) -> c17(A__TL(cons(z0, hd(incr(s(y1)))))) MARK(tl(cons(z0, hd(hd(zeros))))) -> c17(A__TL(cons(z0, hd(hd(zeros))))) MARK(tl(cons(z0, tl(hd(zeros))))) -> c17(A__TL(cons(z0, tl(hd(zeros))))) MARK(tl(cons(z0, tl(adx(0))))) -> c17(A__TL(cons(z0, tl(adx(0))))) MARK(hd(adx(adx(y0)))) -> c16(MARK(adx(adx(y0)))) MARK(hd(adx(incr(y0)))) -> c16(MARK(adx(incr(y0)))) MARK(hd(adx(hd(cons(y0, y1))))) -> c16(MARK(adx(hd(cons(y0, y1))))) MARK(hd(adx(tl(cons(y0, y1))))) -> c16(MARK(adx(tl(cons(y0, y1))))) MARK(hd(adx(hd(adx(nats))))) -> c16(MARK(adx(hd(adx(nats))))) MARK(hd(adx(hd(adx(adx(y0)))))) -> c16(MARK(adx(hd(adx(adx(y0)))))) MARK(hd(adx(hd(adx(zeros))))) -> c16(MARK(adx(hd(adx(zeros))))) MARK(hd(adx(hd(adx(incr(y0)))))) -> c16(MARK(adx(hd(adx(incr(y0)))))) MARK(hd(adx(hd(adx(hd(y0)))))) -> c16(MARK(adx(hd(adx(hd(y0)))))) MARK(hd(adx(hd(adx(tl(y0)))))) -> c16(MARK(adx(hd(adx(tl(y0)))))) MARK(hd(adx(hd(adx(cons(y0, y1)))))) -> c16(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(hd(adx(hd(adx(y0))))) -> c16(MARK(adx(hd(adx(y0))))) MARK(hd(adx(hd(incr(nats))))) -> c16(MARK(adx(hd(incr(nats))))) MARK(hd(adx(hd(incr(adx(y0)))))) -> c16(MARK(adx(hd(incr(adx(y0)))))) MARK(hd(adx(hd(incr(zeros))))) -> c16(MARK(adx(hd(incr(zeros))))) MARK(hd(adx(hd(incr(incr(y0)))))) -> c16(MARK(adx(hd(incr(incr(y0)))))) MARK(hd(adx(hd(incr(hd(y0)))))) -> c16(MARK(adx(hd(incr(hd(y0)))))) MARK(hd(adx(hd(incr(tl(y0)))))) -> c16(MARK(adx(hd(incr(tl(y0)))))) MARK(hd(adx(hd(incr(cons(y0, y1)))))) -> c16(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(hd(adx(hd(incr(y0))))) -> c16(MARK(adx(hd(incr(y0))))) MARK(hd(adx(hd(hd(nats))))) -> c16(MARK(adx(hd(hd(nats))))) MARK(hd(adx(hd(hd(adx(y0)))))) -> c16(MARK(adx(hd(hd(adx(y0)))))) MARK(hd(adx(hd(hd(incr(y0)))))) -> c16(MARK(adx(hd(hd(incr(y0)))))) MARK(hd(adx(hd(hd(hd(y0)))))) -> c16(MARK(adx(hd(hd(hd(y0)))))) MARK(hd(adx(hd(hd(tl(y0)))))) -> c16(MARK(adx(hd(hd(tl(y0)))))) MARK(hd(adx(hd(hd(cons(y0, y1)))))) -> c16(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(hd(adx(hd(hd(y0))))) -> c16(MARK(adx(hd(hd(y0))))) MARK(hd(adx(hd(tl(nats))))) -> c16(MARK(adx(hd(tl(nats))))) MARK(hd(adx(hd(tl(adx(y0)))))) -> c16(MARK(adx(hd(tl(adx(y0)))))) MARK(hd(adx(hd(tl(incr(y0)))))) -> c16(MARK(adx(hd(tl(incr(y0)))))) MARK(hd(adx(hd(tl(hd(y0)))))) -> c16(MARK(adx(hd(tl(hd(y0)))))) MARK(hd(adx(hd(tl(tl(y0)))))) -> c16(MARK(adx(hd(tl(tl(y0)))))) MARK(hd(adx(hd(tl(cons(y0, y1)))))) -> c16(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(hd(adx(hd(tl(y0))))) -> c16(MARK(adx(hd(tl(y0))))) MARK(hd(adx(hd(nats)))) -> c16(MARK(adx(hd(nats)))) MARK(hd(adx(tl(adx(nats))))) -> c16(MARK(adx(tl(adx(nats))))) MARK(hd(adx(tl(adx(adx(y0)))))) -> c16(MARK(adx(tl(adx(adx(y0)))))) MARK(hd(adx(tl(adx(zeros))))) -> c16(MARK(adx(tl(adx(zeros))))) MARK(hd(adx(tl(adx(incr(y0)))))) -> c16(MARK(adx(tl(adx(incr(y0)))))) MARK(hd(adx(tl(adx(hd(y0)))))) -> c16(MARK(adx(tl(adx(hd(y0)))))) MARK(hd(adx(tl(adx(tl(y0)))))) -> c16(MARK(adx(tl(adx(tl(y0)))))) MARK(hd(adx(tl(adx(cons(y0, y1)))))) -> c16(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(hd(adx(tl(adx(y0))))) -> c16(MARK(adx(tl(adx(y0))))) MARK(hd(adx(tl(incr(nats))))) -> c16(MARK(adx(tl(incr(nats))))) MARK(hd(adx(tl(incr(adx(y0)))))) -> c16(MARK(adx(tl(incr(adx(y0)))))) MARK(hd(adx(tl(incr(zeros))))) -> c16(MARK(adx(tl(incr(zeros))))) MARK(hd(adx(tl(incr(incr(y0)))))) -> c16(MARK(adx(tl(incr(incr(y0)))))) MARK(hd(adx(tl(incr(hd(y0)))))) -> c16(MARK(adx(tl(incr(hd(y0)))))) MARK(hd(adx(tl(incr(tl(y0)))))) -> c16(MARK(adx(tl(incr(tl(y0)))))) MARK(hd(adx(tl(incr(cons(y0, y1)))))) -> c16(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(hd(adx(tl(incr(s(y0)))))) -> c16(MARK(adx(tl(incr(s(y0)))))) MARK(hd(adx(tl(incr(y0))))) -> c16(MARK(adx(tl(incr(y0))))) MARK(hd(adx(tl(hd(nats))))) -> c16(MARK(adx(tl(hd(nats))))) MARK(hd(adx(tl(hd(adx(y0)))))) -> c16(MARK(adx(tl(hd(adx(y0)))))) MARK(hd(adx(tl(hd(incr(y0)))))) -> c16(MARK(adx(tl(hd(incr(y0)))))) MARK(hd(adx(tl(hd(hd(y0)))))) -> c16(MARK(adx(tl(hd(hd(y0)))))) MARK(hd(adx(tl(hd(tl(y0)))))) -> c16(MARK(adx(tl(hd(tl(y0)))))) MARK(hd(adx(tl(hd(cons(y0, y1)))))) -> c16(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(hd(adx(tl(hd(y0))))) -> c16(MARK(adx(tl(hd(y0))))) MARK(hd(adx(tl(tl(nats))))) -> c16(MARK(adx(tl(tl(nats))))) MARK(hd(adx(tl(tl(adx(y0)))))) -> c16(MARK(adx(tl(tl(adx(y0)))))) MARK(hd(adx(tl(tl(incr(y0)))))) -> c16(MARK(adx(tl(tl(incr(y0)))))) MARK(hd(adx(tl(tl(hd(y0)))))) -> c16(MARK(adx(tl(tl(hd(y0)))))) MARK(hd(adx(tl(tl(tl(y0)))))) -> c16(MARK(adx(tl(tl(tl(y0)))))) MARK(hd(adx(tl(tl(cons(y0, y1)))))) -> c16(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(hd(adx(tl(tl(y0))))) -> c16(MARK(adx(tl(tl(y0))))) MARK(hd(adx(tl(nats)))) -> c16(MARK(adx(tl(nats)))) MARK(hd(adx(hd(adx(0))))) -> c16(MARK(adx(hd(adx(0))))) MARK(hd(adx(hd(adx(s(y0)))))) -> c16(MARK(adx(hd(adx(s(y0)))))) MARK(hd(adx(hd(incr(0))))) -> c16(MARK(adx(hd(incr(0))))) MARK(hd(adx(hd(incr(s(y0)))))) -> c16(MARK(adx(hd(incr(s(y0)))))) MARK(hd(adx(hd(hd(zeros))))) -> c16(MARK(adx(hd(hd(zeros))))) MARK(hd(adx(tl(hd(zeros))))) -> c16(MARK(adx(tl(hd(zeros))))) MARK(hd(adx(tl(adx(0))))) -> c16(MARK(adx(tl(adx(0))))) MARK(hd(adx(hd(tl(zeros))))) -> c16(MARK(adx(hd(tl(zeros))))) MARK(hd(adx(tl(tl(zeros))))) -> c16(MARK(adx(tl(tl(zeros))))) MARK(hd(adx(tl(adx(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) MARK(hd(adx(tl(incr(0))))) -> c16(MARK(adx(tl(incr(0))))) S tuples: MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, 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A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, 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MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) MARK(tl(cons(z0, adx(y1)))) -> c17(A__TL(cons(z0, adx(y1)))) MARK(tl(cons(z0, incr(y1)))) -> c17(A__TL(cons(z0, incr(y1)))) MARK(tl(cons(z0, hd(cons(y1, y2))))) -> c17(A__TL(cons(z0, hd(cons(y1, y2))))) MARK(tl(cons(z0, tl(cons(y1, y2))))) -> c17(A__TL(cons(z0, tl(cons(y1, y2))))) MARK(tl(cons(z0, hd(adx(nats))))) -> c17(A__TL(cons(z0, hd(adx(nats))))) MARK(tl(cons(z0, hd(adx(adx(y1)))))) -> c17(A__TL(cons(z0, hd(adx(adx(y1)))))) MARK(tl(cons(z0, hd(adx(zeros))))) -> c17(A__TL(cons(z0, hd(adx(zeros))))) MARK(tl(cons(z0, hd(adx(incr(y1)))))) -> c17(A__TL(cons(z0, hd(adx(incr(y1)))))) MARK(tl(cons(z0, hd(adx(hd(y1)))))) -> c17(A__TL(cons(z0, hd(adx(hd(y1)))))) MARK(tl(cons(z0, hd(adx(tl(y1)))))) -> c17(A__TL(cons(z0, hd(adx(tl(y1)))))) MARK(tl(cons(z0, hd(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(adx(cons(y1, y2)))))) MARK(tl(cons(z0, hd(adx(y1))))) -> c17(A__TL(cons(z0, hd(adx(y1))))) MARK(tl(cons(z0, hd(incr(nats))))) -> c17(A__TL(cons(z0, hd(incr(nats))))) MARK(tl(cons(z0, hd(incr(adx(y1)))))) -> c17(A__TL(cons(z0, hd(incr(adx(y1)))))) MARK(tl(cons(z0, hd(incr(zeros))))) -> c17(A__TL(cons(z0, hd(incr(zeros))))) MARK(tl(cons(z0, hd(incr(incr(y1)))))) -> c17(A__TL(cons(z0, hd(incr(incr(y1)))))) MARK(tl(cons(z0, hd(incr(hd(y1)))))) -> c17(A__TL(cons(z0, hd(incr(hd(y1)))))) MARK(tl(cons(z0, hd(incr(tl(y1)))))) -> c17(A__TL(cons(z0, hd(incr(tl(y1)))))) MARK(tl(cons(z0, hd(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(incr(cons(y1, y2)))))) MARK(tl(cons(z0, hd(incr(y1))))) -> c17(A__TL(cons(z0, hd(incr(y1))))) MARK(tl(cons(z0, hd(hd(nats))))) -> c17(A__TL(cons(z0, hd(hd(nats))))) MARK(tl(cons(z0, hd(hd(adx(y1)))))) -> c17(A__TL(cons(z0, hd(hd(adx(y1)))))) MARK(tl(cons(z0, hd(hd(incr(y1)))))) -> c17(A__TL(cons(z0, hd(hd(incr(y1)))))) MARK(tl(cons(z0, hd(hd(hd(y1)))))) -> c17(A__TL(cons(z0, hd(hd(hd(y1)))))) MARK(tl(cons(z0, hd(hd(tl(y1)))))) -> c17(A__TL(cons(z0, hd(hd(tl(y1)))))) MARK(tl(cons(z0, hd(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(hd(cons(y1, y2)))))) MARK(tl(cons(z0, hd(hd(y1))))) -> c17(A__TL(cons(z0, hd(hd(y1))))) MARK(tl(cons(z0, hd(tl(nats))))) -> c17(A__TL(cons(z0, hd(tl(nats))))) MARK(tl(cons(z0, hd(tl(adx(y1)))))) -> c17(A__TL(cons(z0, hd(tl(adx(y1)))))) MARK(tl(cons(z0, hd(tl(zeros))))) -> c17(A__TL(cons(z0, hd(tl(zeros))))) MARK(tl(cons(z0, hd(tl(incr(y1)))))) -> c17(A__TL(cons(z0, hd(tl(incr(y1)))))) MARK(tl(cons(z0, hd(tl(hd(y1)))))) -> c17(A__TL(cons(z0, hd(tl(hd(y1)))))) MARK(tl(cons(z0, hd(tl(tl(y1)))))) -> c17(A__TL(cons(z0, hd(tl(tl(y1)))))) MARK(tl(cons(z0, hd(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(tl(cons(y1, y2)))))) MARK(tl(cons(z0, hd(tl(y1))))) -> c17(A__TL(cons(z0, hd(tl(y1))))) MARK(tl(cons(z0, hd(nats)))) -> c17(A__TL(cons(z0, hd(nats)))) MARK(tl(cons(z0, tl(adx(nats))))) -> c17(A__TL(cons(z0, tl(adx(nats))))) MARK(tl(cons(z0, tl(adx(adx(y1)))))) -> c17(A__TL(cons(z0, tl(adx(adx(y1)))))) MARK(tl(cons(z0, tl(adx(zeros))))) -> c17(A__TL(cons(z0, tl(adx(zeros))))) MARK(tl(cons(z0, tl(adx(incr(y1)))))) -> c17(A__TL(cons(z0, tl(adx(incr(y1)))))) MARK(tl(cons(z0, tl(adx(hd(y1)))))) -> c17(A__TL(cons(z0, tl(adx(hd(y1)))))) MARK(tl(cons(z0, tl(adx(tl(y1)))))) -> c17(A__TL(cons(z0, tl(adx(tl(y1)))))) MARK(tl(cons(z0, tl(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(adx(cons(y1, y2)))))) MARK(tl(cons(z0, tl(adx(s(y1)))))) -> c17(A__TL(cons(z0, tl(adx(s(y1)))))) MARK(tl(cons(z0, tl(adx(y1))))) -> c17(A__TL(cons(z0, tl(adx(y1))))) MARK(tl(cons(z0, tl(incr(nats))))) -> c17(A__TL(cons(z0, tl(incr(nats))))) MARK(tl(cons(z0, tl(incr(adx(y1)))))) -> c17(A__TL(cons(z0, tl(incr(adx(y1)))))) MARK(tl(cons(z0, tl(incr(zeros))))) -> c17(A__TL(cons(z0, tl(incr(zeros))))) MARK(tl(cons(z0, tl(incr(incr(y1)))))) -> c17(A__TL(cons(z0, tl(incr(incr(y1)))))) MARK(tl(cons(z0, tl(incr(hd(y1)))))) -> c17(A__TL(cons(z0, tl(incr(hd(y1)))))) MARK(tl(cons(z0, tl(incr(tl(y1)))))) -> c17(A__TL(cons(z0, tl(incr(tl(y1)))))) MARK(tl(cons(z0, tl(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(incr(cons(y1, y2)))))) MARK(tl(cons(z0, tl(incr(0))))) -> c17(A__TL(cons(z0, tl(incr(0))))) MARK(tl(cons(z0, tl(incr(s(y1)))))) -> c17(A__TL(cons(z0, tl(incr(s(y1)))))) MARK(tl(cons(z0, tl(incr(y1))))) -> c17(A__TL(cons(z0, tl(incr(y1))))) MARK(tl(cons(z0, tl(hd(nats))))) -> c17(A__TL(cons(z0, tl(hd(nats))))) MARK(tl(cons(z0, tl(hd(adx(y1)))))) -> c17(A__TL(cons(z0, tl(hd(adx(y1)))))) MARK(tl(cons(z0, tl(hd(incr(y1)))))) -> c17(A__TL(cons(z0, tl(hd(incr(y1)))))) MARK(tl(cons(z0, tl(hd(hd(y1)))))) -> c17(A__TL(cons(z0, tl(hd(hd(y1)))))) MARK(tl(cons(z0, tl(hd(tl(y1)))))) -> c17(A__TL(cons(z0, tl(hd(tl(y1)))))) MARK(tl(cons(z0, tl(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(hd(cons(y1, y2)))))) MARK(tl(cons(z0, tl(hd(y1))))) -> c17(A__TL(cons(z0, tl(hd(y1))))) MARK(tl(cons(z0, tl(tl(nats))))) -> c17(A__TL(cons(z0, tl(tl(nats))))) MARK(tl(cons(z0, tl(tl(adx(y1)))))) -> c17(A__TL(cons(z0, tl(tl(adx(y1)))))) MARK(tl(cons(z0, tl(tl(zeros))))) -> c17(A__TL(cons(z0, tl(tl(zeros))))) MARK(tl(cons(z0, tl(tl(incr(y1)))))) -> c17(A__TL(cons(z0, tl(tl(incr(y1)))))) MARK(tl(cons(z0, tl(tl(hd(y1)))))) -> c17(A__TL(cons(z0, tl(tl(hd(y1)))))) MARK(tl(cons(z0, tl(tl(tl(y1)))))) -> c17(A__TL(cons(z0, tl(tl(tl(y1)))))) MARK(tl(cons(z0, tl(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(tl(cons(y1, y2)))))) MARK(tl(cons(z0, tl(tl(y1))))) -> c17(A__TL(cons(z0, tl(tl(y1))))) MARK(tl(cons(z0, tl(nats)))) -> c17(A__TL(cons(z0, tl(nats)))) MARK(tl(cons(z0, hd(adx(0))))) -> c17(A__TL(cons(z0, hd(adx(0))))) MARK(tl(cons(z0, hd(adx(s(y1)))))) -> c17(A__TL(cons(z0, hd(adx(s(y1)))))) MARK(tl(cons(z0, hd(incr(0))))) -> c17(A__TL(cons(z0, hd(incr(0))))) MARK(tl(cons(z0, hd(incr(s(y1)))))) -> c17(A__TL(cons(z0, hd(incr(s(y1)))))) MARK(tl(cons(z0, hd(hd(zeros))))) -> c17(A__TL(cons(z0, hd(hd(zeros))))) MARK(tl(cons(z0, tl(hd(zeros))))) -> c17(A__TL(cons(z0, tl(hd(zeros))))) MARK(tl(cons(z0, tl(adx(0))))) -> c17(A__TL(cons(z0, tl(adx(0))))) MARK(hd(adx(adx(y0)))) -> c16(MARK(adx(adx(y0)))) MARK(hd(adx(incr(y0)))) -> c16(MARK(adx(incr(y0)))) MARK(hd(adx(hd(cons(y0, y1))))) -> c16(MARK(adx(hd(cons(y0, y1))))) MARK(hd(adx(tl(cons(y0, y1))))) -> c16(MARK(adx(tl(cons(y0, y1))))) MARK(hd(adx(hd(adx(nats))))) -> c16(MARK(adx(hd(adx(nats))))) MARK(hd(adx(hd(adx(adx(y0)))))) -> c16(MARK(adx(hd(adx(adx(y0)))))) MARK(hd(adx(hd(adx(zeros))))) -> c16(MARK(adx(hd(adx(zeros))))) MARK(hd(adx(hd(adx(incr(y0)))))) -> c16(MARK(adx(hd(adx(incr(y0)))))) MARK(hd(adx(hd(adx(hd(y0)))))) -> c16(MARK(adx(hd(adx(hd(y0)))))) MARK(hd(adx(hd(adx(tl(y0)))))) -> c16(MARK(adx(hd(adx(tl(y0)))))) MARK(hd(adx(hd(adx(cons(y0, y1)))))) -> c16(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(hd(adx(hd(adx(y0))))) -> c16(MARK(adx(hd(adx(y0))))) MARK(hd(adx(hd(incr(nats))))) -> c16(MARK(adx(hd(incr(nats))))) MARK(hd(adx(hd(incr(adx(y0)))))) -> c16(MARK(adx(hd(incr(adx(y0)))))) MARK(hd(adx(hd(incr(zeros))))) -> c16(MARK(adx(hd(incr(zeros))))) MARK(hd(adx(hd(incr(incr(y0)))))) -> c16(MARK(adx(hd(incr(incr(y0)))))) MARK(hd(adx(hd(incr(hd(y0)))))) -> c16(MARK(adx(hd(incr(hd(y0)))))) MARK(hd(adx(hd(incr(tl(y0)))))) -> c16(MARK(adx(hd(incr(tl(y0)))))) MARK(hd(adx(hd(incr(cons(y0, y1)))))) -> c16(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(hd(adx(hd(incr(y0))))) -> c16(MARK(adx(hd(incr(y0))))) MARK(hd(adx(hd(hd(nats))))) -> c16(MARK(adx(hd(hd(nats))))) MARK(hd(adx(hd(hd(adx(y0)))))) -> c16(MARK(adx(hd(hd(adx(y0)))))) MARK(hd(adx(hd(hd(incr(y0)))))) -> c16(MARK(adx(hd(hd(incr(y0)))))) MARK(hd(adx(hd(hd(hd(y0)))))) -> c16(MARK(adx(hd(hd(hd(y0)))))) MARK(hd(adx(hd(hd(tl(y0)))))) -> c16(MARK(adx(hd(hd(tl(y0)))))) MARK(hd(adx(hd(hd(cons(y0, y1)))))) -> c16(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(hd(adx(hd(hd(y0))))) -> c16(MARK(adx(hd(hd(y0))))) MARK(hd(adx(hd(tl(nats))))) -> c16(MARK(adx(hd(tl(nats))))) MARK(hd(adx(hd(tl(adx(y0)))))) -> c16(MARK(adx(hd(tl(adx(y0)))))) MARK(hd(adx(hd(tl(incr(y0)))))) -> c16(MARK(adx(hd(tl(incr(y0)))))) MARK(hd(adx(hd(tl(hd(y0)))))) -> c16(MARK(adx(hd(tl(hd(y0)))))) MARK(hd(adx(hd(tl(tl(y0)))))) -> c16(MARK(adx(hd(tl(tl(y0)))))) MARK(hd(adx(hd(tl(cons(y0, y1)))))) -> c16(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(hd(adx(hd(tl(y0))))) -> c16(MARK(adx(hd(tl(y0))))) MARK(hd(adx(hd(nats)))) -> c16(MARK(adx(hd(nats)))) MARK(hd(adx(tl(adx(nats))))) -> c16(MARK(adx(tl(adx(nats))))) MARK(hd(adx(tl(adx(adx(y0)))))) -> c16(MARK(adx(tl(adx(adx(y0)))))) MARK(hd(adx(tl(adx(zeros))))) -> c16(MARK(adx(tl(adx(zeros))))) MARK(hd(adx(tl(adx(incr(y0)))))) -> c16(MARK(adx(tl(adx(incr(y0)))))) MARK(hd(adx(tl(adx(hd(y0)))))) -> c16(MARK(adx(tl(adx(hd(y0)))))) MARK(hd(adx(tl(adx(tl(y0)))))) -> c16(MARK(adx(tl(adx(tl(y0)))))) MARK(hd(adx(tl(adx(cons(y0, y1)))))) -> c16(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(hd(adx(tl(adx(y0))))) -> c16(MARK(adx(tl(adx(y0))))) MARK(hd(adx(tl(incr(nats))))) -> c16(MARK(adx(tl(incr(nats))))) MARK(hd(adx(tl(incr(adx(y0)))))) -> c16(MARK(adx(tl(incr(adx(y0)))))) MARK(hd(adx(tl(incr(zeros))))) -> c16(MARK(adx(tl(incr(zeros))))) MARK(hd(adx(tl(incr(incr(y0)))))) -> c16(MARK(adx(tl(incr(incr(y0)))))) MARK(hd(adx(tl(incr(hd(y0)))))) -> c16(MARK(adx(tl(incr(hd(y0)))))) MARK(hd(adx(tl(incr(tl(y0)))))) -> c16(MARK(adx(tl(incr(tl(y0)))))) MARK(hd(adx(tl(incr(cons(y0, y1)))))) -> c16(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(hd(adx(tl(incr(s(y0)))))) -> c16(MARK(adx(tl(incr(s(y0)))))) MARK(hd(adx(tl(incr(y0))))) -> c16(MARK(adx(tl(incr(y0))))) MARK(hd(adx(tl(hd(nats))))) -> c16(MARK(adx(tl(hd(nats))))) MARK(hd(adx(tl(hd(adx(y0)))))) -> c16(MARK(adx(tl(hd(adx(y0)))))) MARK(hd(adx(tl(hd(incr(y0)))))) -> c16(MARK(adx(tl(hd(incr(y0)))))) MARK(hd(adx(tl(hd(hd(y0)))))) -> c16(MARK(adx(tl(hd(hd(y0)))))) MARK(hd(adx(tl(hd(tl(y0)))))) -> c16(MARK(adx(tl(hd(tl(y0)))))) MARK(hd(adx(tl(hd(cons(y0, y1)))))) -> c16(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(hd(adx(tl(hd(y0))))) -> c16(MARK(adx(tl(hd(y0))))) MARK(hd(adx(tl(tl(nats))))) -> c16(MARK(adx(tl(tl(nats))))) MARK(hd(adx(tl(tl(adx(y0)))))) -> c16(MARK(adx(tl(tl(adx(y0)))))) MARK(hd(adx(tl(tl(incr(y0)))))) -> c16(MARK(adx(tl(tl(incr(y0)))))) MARK(hd(adx(tl(tl(hd(y0)))))) -> c16(MARK(adx(tl(tl(hd(y0)))))) MARK(hd(adx(tl(tl(tl(y0)))))) -> c16(MARK(adx(tl(tl(tl(y0)))))) MARK(hd(adx(tl(tl(cons(y0, y1)))))) -> c16(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(hd(adx(tl(tl(y0))))) -> c16(MARK(adx(tl(tl(y0))))) MARK(hd(adx(tl(nats)))) -> c16(MARK(adx(tl(nats)))) MARK(hd(adx(hd(adx(0))))) -> c16(MARK(adx(hd(adx(0))))) MARK(hd(adx(hd(adx(s(y0)))))) -> c16(MARK(adx(hd(adx(s(y0)))))) MARK(hd(adx(hd(incr(0))))) -> c16(MARK(adx(hd(incr(0))))) MARK(hd(adx(hd(incr(s(y0)))))) -> c16(MARK(adx(hd(incr(s(y0)))))) MARK(hd(adx(hd(hd(zeros))))) -> c16(MARK(adx(hd(hd(zeros))))) MARK(hd(adx(tl(hd(zeros))))) -> c16(MARK(adx(tl(hd(zeros))))) MARK(hd(adx(tl(adx(0))))) -> c16(MARK(adx(tl(adx(0))))) MARK(hd(adx(hd(tl(zeros))))) -> c16(MARK(adx(hd(tl(zeros))))) MARK(hd(adx(tl(tl(zeros))))) -> c16(MARK(adx(tl(tl(zeros))))) MARK(hd(adx(tl(adx(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) MARK(hd(adx(tl(incr(0))))) -> c16(MARK(adx(tl(incr(0))))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c16_2, c16_1, c17_2, c17_1, c8_1, c10_1, c13_1, c15_1 ---------------------------------------- (203) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(hd(adx(x0))) -> c16(MARK(adx(x0))) by MARK(hd(adx(adx(y0)))) -> c16(MARK(adx(adx(y0)))) MARK(hd(adx(incr(y0)))) -> c16(MARK(adx(incr(y0)))) MARK(hd(adx(hd(cons(y0, y1))))) -> c16(MARK(adx(hd(cons(y0, y1))))) MARK(hd(adx(tl(cons(y0, y1))))) -> c16(MARK(adx(tl(cons(y0, y1))))) MARK(hd(adx(hd(adx(nats))))) -> c16(MARK(adx(hd(adx(nats))))) MARK(hd(adx(hd(adx(adx(y0)))))) -> c16(MARK(adx(hd(adx(adx(y0)))))) MARK(hd(adx(hd(adx(zeros))))) -> c16(MARK(adx(hd(adx(zeros))))) MARK(hd(adx(hd(adx(incr(y0)))))) -> c16(MARK(adx(hd(adx(incr(y0)))))) MARK(hd(adx(hd(adx(hd(y0)))))) -> c16(MARK(adx(hd(adx(hd(y0)))))) MARK(hd(adx(hd(adx(tl(y0)))))) -> c16(MARK(adx(hd(adx(tl(y0)))))) MARK(hd(adx(hd(adx(cons(y0, y1)))))) -> c16(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(hd(adx(hd(adx(y0))))) -> c16(MARK(adx(hd(adx(y0))))) MARK(hd(adx(hd(incr(nats))))) -> c16(MARK(adx(hd(incr(nats))))) MARK(hd(adx(hd(incr(adx(y0)))))) -> c16(MARK(adx(hd(incr(adx(y0)))))) MARK(hd(adx(hd(incr(zeros))))) -> c16(MARK(adx(hd(incr(zeros))))) MARK(hd(adx(hd(incr(incr(y0)))))) -> c16(MARK(adx(hd(incr(incr(y0)))))) MARK(hd(adx(hd(incr(hd(y0)))))) -> c16(MARK(adx(hd(incr(hd(y0)))))) MARK(hd(adx(hd(incr(tl(y0)))))) -> c16(MARK(adx(hd(incr(tl(y0)))))) MARK(hd(adx(hd(incr(cons(y0, y1)))))) -> c16(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(hd(adx(hd(incr(y0))))) -> c16(MARK(adx(hd(incr(y0))))) MARK(hd(adx(hd(hd(nats))))) -> c16(MARK(adx(hd(hd(nats))))) MARK(hd(adx(hd(hd(adx(y0)))))) -> c16(MARK(adx(hd(hd(adx(y0)))))) MARK(hd(adx(hd(hd(incr(y0)))))) -> c16(MARK(adx(hd(hd(incr(y0)))))) MARK(hd(adx(hd(hd(hd(y0)))))) -> c16(MARK(adx(hd(hd(hd(y0)))))) MARK(hd(adx(hd(hd(tl(y0)))))) -> c16(MARK(adx(hd(hd(tl(y0)))))) MARK(hd(adx(hd(hd(cons(y0, y1)))))) -> c16(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(hd(adx(hd(hd(y0))))) -> c16(MARK(adx(hd(hd(y0))))) MARK(hd(adx(hd(tl(nats))))) -> c16(MARK(adx(hd(tl(nats))))) MARK(hd(adx(hd(tl(adx(y0)))))) -> c16(MARK(adx(hd(tl(adx(y0)))))) MARK(hd(adx(hd(tl(incr(y0)))))) -> c16(MARK(adx(hd(tl(incr(y0)))))) MARK(hd(adx(hd(tl(hd(y0)))))) -> c16(MARK(adx(hd(tl(hd(y0)))))) MARK(hd(adx(hd(tl(tl(y0)))))) -> c16(MARK(adx(hd(tl(tl(y0)))))) MARK(hd(adx(hd(tl(cons(y0, y1)))))) -> c16(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(hd(adx(hd(tl(y0))))) -> c16(MARK(adx(hd(tl(y0))))) MARK(hd(adx(hd(nats)))) -> c16(MARK(adx(hd(nats)))) MARK(hd(adx(tl(adx(nats))))) -> c16(MARK(adx(tl(adx(nats))))) MARK(hd(adx(tl(adx(adx(y0)))))) -> c16(MARK(adx(tl(adx(adx(y0)))))) MARK(hd(adx(tl(adx(zeros))))) -> c16(MARK(adx(tl(adx(zeros))))) MARK(hd(adx(tl(adx(incr(y0)))))) -> c16(MARK(adx(tl(adx(incr(y0)))))) MARK(hd(adx(tl(adx(hd(y0)))))) -> c16(MARK(adx(tl(adx(hd(y0)))))) MARK(hd(adx(tl(adx(tl(y0)))))) -> c16(MARK(adx(tl(adx(tl(y0)))))) MARK(hd(adx(tl(adx(cons(y0, y1)))))) -> c16(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(hd(adx(tl(adx(y0))))) -> c16(MARK(adx(tl(adx(y0))))) MARK(hd(adx(tl(incr(nats))))) -> c16(MARK(adx(tl(incr(nats))))) MARK(hd(adx(tl(incr(adx(y0)))))) -> c16(MARK(adx(tl(incr(adx(y0)))))) MARK(hd(adx(tl(incr(zeros))))) -> c16(MARK(adx(tl(incr(zeros))))) MARK(hd(adx(tl(incr(incr(y0)))))) -> c16(MARK(adx(tl(incr(incr(y0)))))) MARK(hd(adx(tl(incr(hd(y0)))))) -> c16(MARK(adx(tl(incr(hd(y0)))))) MARK(hd(adx(tl(incr(tl(y0)))))) -> c16(MARK(adx(tl(incr(tl(y0)))))) MARK(hd(adx(tl(incr(cons(y0, y1)))))) -> c16(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(hd(adx(tl(incr(s(y0)))))) -> c16(MARK(adx(tl(incr(s(y0)))))) MARK(hd(adx(tl(incr(y0))))) -> c16(MARK(adx(tl(incr(y0))))) MARK(hd(adx(tl(hd(nats))))) -> c16(MARK(adx(tl(hd(nats))))) MARK(hd(adx(tl(hd(adx(y0)))))) -> c16(MARK(adx(tl(hd(adx(y0)))))) MARK(hd(adx(tl(hd(incr(y0)))))) -> c16(MARK(adx(tl(hd(incr(y0)))))) MARK(hd(adx(tl(hd(hd(y0)))))) -> c16(MARK(adx(tl(hd(hd(y0)))))) MARK(hd(adx(tl(hd(tl(y0)))))) -> c16(MARK(adx(tl(hd(tl(y0)))))) MARK(hd(adx(tl(hd(cons(y0, y1)))))) -> c16(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(hd(adx(tl(hd(y0))))) -> c16(MARK(adx(tl(hd(y0))))) MARK(hd(adx(tl(tl(nats))))) -> c16(MARK(adx(tl(tl(nats))))) MARK(hd(adx(tl(tl(adx(y0)))))) -> c16(MARK(adx(tl(tl(adx(y0)))))) MARK(hd(adx(tl(tl(incr(y0)))))) -> c16(MARK(adx(tl(tl(incr(y0)))))) MARK(hd(adx(tl(tl(hd(y0)))))) -> c16(MARK(adx(tl(tl(hd(y0)))))) MARK(hd(adx(tl(tl(tl(y0)))))) -> c16(MARK(adx(tl(tl(tl(y0)))))) MARK(hd(adx(tl(tl(cons(y0, y1)))))) -> c16(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(hd(adx(tl(tl(y0))))) -> c16(MARK(adx(tl(tl(y0))))) MARK(hd(adx(tl(nats)))) -> c16(MARK(adx(tl(nats)))) MARK(hd(adx(hd(adx(0))))) -> c16(MARK(adx(hd(adx(0))))) MARK(hd(adx(hd(adx(s(y0)))))) -> c16(MARK(adx(hd(adx(s(y0)))))) MARK(hd(adx(hd(incr(0))))) -> c16(MARK(adx(hd(incr(0))))) MARK(hd(adx(hd(incr(s(y0)))))) -> c16(MARK(adx(hd(incr(s(y0)))))) MARK(hd(adx(hd(hd(zeros))))) -> c16(MARK(adx(hd(hd(zeros))))) MARK(hd(adx(tl(hd(zeros))))) -> c16(MARK(adx(tl(hd(zeros))))) MARK(hd(adx(tl(adx(0))))) -> c16(MARK(adx(tl(adx(0))))) MARK(hd(adx(hd(tl(zeros))))) -> c16(MARK(adx(hd(tl(zeros))))) MARK(hd(adx(tl(tl(zeros))))) -> c16(MARK(adx(tl(tl(zeros))))) MARK(hd(adx(tl(adx(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) MARK(hd(adx(tl(incr(0))))) -> c16(MARK(adx(tl(incr(0))))) ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> 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c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) MARK(tl(cons(z0, adx(y1)))) -> c17(A__TL(cons(z0, adx(y1)))) MARK(tl(cons(z0, incr(y1)))) -> c17(A__TL(cons(z0, incr(y1)))) MARK(tl(cons(z0, hd(cons(y1, y2))))) -> c17(A__TL(cons(z0, hd(cons(y1, y2))))) MARK(tl(cons(z0, tl(cons(y1, y2))))) -> c17(A__TL(cons(z0, tl(cons(y1, y2))))) MARK(tl(cons(z0, hd(adx(nats))))) -> c17(A__TL(cons(z0, hd(adx(nats))))) MARK(tl(cons(z0, hd(adx(adx(y1)))))) -> c17(A__TL(cons(z0, hd(adx(adx(y1)))))) MARK(tl(cons(z0, hd(adx(zeros))))) -> c17(A__TL(cons(z0, hd(adx(zeros))))) MARK(tl(cons(z0, hd(adx(incr(y1)))))) -> c17(A__TL(cons(z0, hd(adx(incr(y1)))))) MARK(tl(cons(z0, hd(adx(hd(y1)))))) -> c17(A__TL(cons(z0, hd(adx(hd(y1)))))) MARK(tl(cons(z0, hd(adx(tl(y1)))))) -> c17(A__TL(cons(z0, hd(adx(tl(y1)))))) MARK(tl(cons(z0, hd(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(adx(cons(y1, y2)))))) MARK(tl(cons(z0, hd(adx(y1))))) -> c17(A__TL(cons(z0, hd(adx(y1))))) MARK(tl(cons(z0, hd(incr(nats))))) -> c17(A__TL(cons(z0, hd(incr(nats))))) MARK(tl(cons(z0, hd(incr(adx(y1)))))) -> c17(A__TL(cons(z0, hd(incr(adx(y1)))))) MARK(tl(cons(z0, hd(incr(zeros))))) -> c17(A__TL(cons(z0, hd(incr(zeros))))) MARK(tl(cons(z0, hd(incr(incr(y1)))))) -> c17(A__TL(cons(z0, hd(incr(incr(y1)))))) MARK(tl(cons(z0, hd(incr(hd(y1)))))) -> c17(A__TL(cons(z0, hd(incr(hd(y1)))))) MARK(tl(cons(z0, hd(incr(tl(y1)))))) -> c17(A__TL(cons(z0, hd(incr(tl(y1)))))) MARK(tl(cons(z0, hd(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(incr(cons(y1, y2)))))) MARK(tl(cons(z0, hd(incr(y1))))) -> c17(A__TL(cons(z0, hd(incr(y1))))) MARK(tl(cons(z0, hd(hd(nats))))) -> c17(A__TL(cons(z0, hd(hd(nats))))) MARK(tl(cons(z0, hd(hd(adx(y1)))))) -> c17(A__TL(cons(z0, hd(hd(adx(y1)))))) MARK(tl(cons(z0, hd(hd(incr(y1)))))) -> c17(A__TL(cons(z0, hd(hd(incr(y1)))))) MARK(tl(cons(z0, hd(hd(hd(y1)))))) -> c17(A__TL(cons(z0, hd(hd(hd(y1)))))) MARK(tl(cons(z0, hd(hd(tl(y1)))))) -> c17(A__TL(cons(z0, hd(hd(tl(y1)))))) MARK(tl(cons(z0, hd(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(hd(cons(y1, y2)))))) MARK(tl(cons(z0, hd(hd(y1))))) -> c17(A__TL(cons(z0, hd(hd(y1))))) MARK(tl(cons(z0, hd(tl(nats))))) -> c17(A__TL(cons(z0, hd(tl(nats))))) MARK(tl(cons(z0, hd(tl(adx(y1)))))) -> c17(A__TL(cons(z0, hd(tl(adx(y1)))))) MARK(tl(cons(z0, hd(tl(zeros))))) -> c17(A__TL(cons(z0, hd(tl(zeros))))) MARK(tl(cons(z0, hd(tl(incr(y1)))))) -> c17(A__TL(cons(z0, hd(tl(incr(y1)))))) MARK(tl(cons(z0, hd(tl(hd(y1)))))) -> c17(A__TL(cons(z0, hd(tl(hd(y1)))))) MARK(tl(cons(z0, hd(tl(tl(y1)))))) -> c17(A__TL(cons(z0, hd(tl(tl(y1)))))) MARK(tl(cons(z0, hd(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(tl(cons(y1, y2)))))) MARK(tl(cons(z0, hd(tl(y1))))) -> c17(A__TL(cons(z0, hd(tl(y1))))) MARK(tl(cons(z0, hd(nats)))) -> c17(A__TL(cons(z0, hd(nats)))) MARK(tl(cons(z0, tl(adx(nats))))) -> c17(A__TL(cons(z0, tl(adx(nats))))) MARK(tl(cons(z0, tl(adx(adx(y1)))))) -> c17(A__TL(cons(z0, tl(adx(adx(y1)))))) MARK(tl(cons(z0, tl(adx(zeros))))) -> c17(A__TL(cons(z0, tl(adx(zeros))))) MARK(tl(cons(z0, tl(adx(incr(y1)))))) -> c17(A__TL(cons(z0, tl(adx(incr(y1)))))) MARK(tl(cons(z0, tl(adx(hd(y1)))))) -> c17(A__TL(cons(z0, tl(adx(hd(y1)))))) MARK(tl(cons(z0, tl(adx(tl(y1)))))) -> c17(A__TL(cons(z0, tl(adx(tl(y1)))))) MARK(tl(cons(z0, tl(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(adx(cons(y1, y2)))))) MARK(tl(cons(z0, tl(adx(s(y1)))))) -> c17(A__TL(cons(z0, tl(adx(s(y1)))))) MARK(tl(cons(z0, tl(adx(y1))))) -> c17(A__TL(cons(z0, tl(adx(y1))))) MARK(tl(cons(z0, tl(incr(nats))))) -> c17(A__TL(cons(z0, tl(incr(nats))))) MARK(tl(cons(z0, tl(incr(adx(y1)))))) -> c17(A__TL(cons(z0, tl(incr(adx(y1)))))) MARK(tl(cons(z0, tl(incr(zeros))))) -> c17(A__TL(cons(z0, tl(incr(zeros))))) MARK(tl(cons(z0, tl(incr(incr(y1)))))) -> c17(A__TL(cons(z0, tl(incr(incr(y1)))))) MARK(tl(cons(z0, tl(incr(hd(y1)))))) -> c17(A__TL(cons(z0, tl(incr(hd(y1)))))) MARK(tl(cons(z0, tl(incr(tl(y1)))))) -> c17(A__TL(cons(z0, tl(incr(tl(y1)))))) MARK(tl(cons(z0, tl(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(incr(cons(y1, y2)))))) MARK(tl(cons(z0, tl(incr(0))))) -> c17(A__TL(cons(z0, tl(incr(0))))) MARK(tl(cons(z0, tl(incr(s(y1)))))) -> c17(A__TL(cons(z0, tl(incr(s(y1)))))) MARK(tl(cons(z0, tl(incr(y1))))) -> c17(A__TL(cons(z0, tl(incr(y1))))) MARK(tl(cons(z0, tl(hd(nats))))) -> c17(A__TL(cons(z0, tl(hd(nats))))) MARK(tl(cons(z0, tl(hd(adx(y1)))))) -> c17(A__TL(cons(z0, tl(hd(adx(y1)))))) MARK(tl(cons(z0, tl(hd(incr(y1)))))) -> c17(A__TL(cons(z0, tl(hd(incr(y1)))))) MARK(tl(cons(z0, tl(hd(hd(y1)))))) -> c17(A__TL(cons(z0, tl(hd(hd(y1)))))) MARK(tl(cons(z0, tl(hd(tl(y1)))))) -> c17(A__TL(cons(z0, tl(hd(tl(y1)))))) MARK(tl(cons(z0, tl(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(hd(cons(y1, y2)))))) MARK(tl(cons(z0, tl(hd(y1))))) -> c17(A__TL(cons(z0, tl(hd(y1))))) MARK(tl(cons(z0, tl(tl(nats))))) -> c17(A__TL(cons(z0, tl(tl(nats))))) MARK(tl(cons(z0, tl(tl(adx(y1)))))) -> c17(A__TL(cons(z0, tl(tl(adx(y1)))))) MARK(tl(cons(z0, tl(tl(zeros))))) -> c17(A__TL(cons(z0, tl(tl(zeros))))) MARK(tl(cons(z0, tl(tl(incr(y1)))))) -> c17(A__TL(cons(z0, tl(tl(incr(y1)))))) MARK(tl(cons(z0, tl(tl(hd(y1)))))) -> c17(A__TL(cons(z0, tl(tl(hd(y1)))))) MARK(tl(cons(z0, tl(tl(tl(y1)))))) -> c17(A__TL(cons(z0, tl(tl(tl(y1)))))) MARK(tl(cons(z0, tl(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(tl(cons(y1, y2)))))) MARK(tl(cons(z0, tl(tl(y1))))) -> c17(A__TL(cons(z0, tl(tl(y1))))) MARK(tl(cons(z0, tl(nats)))) -> c17(A__TL(cons(z0, tl(nats)))) MARK(tl(cons(z0, hd(adx(0))))) -> c17(A__TL(cons(z0, hd(adx(0))))) MARK(tl(cons(z0, hd(adx(s(y1)))))) -> c17(A__TL(cons(z0, hd(adx(s(y1)))))) MARK(tl(cons(z0, hd(incr(0))))) -> c17(A__TL(cons(z0, hd(incr(0))))) MARK(tl(cons(z0, hd(incr(s(y1)))))) -> c17(A__TL(cons(z0, hd(incr(s(y1)))))) MARK(tl(cons(z0, hd(hd(zeros))))) -> c17(A__TL(cons(z0, hd(hd(zeros))))) MARK(tl(cons(z0, tl(hd(zeros))))) -> c17(A__TL(cons(z0, tl(hd(zeros))))) MARK(tl(cons(z0, tl(adx(0))))) -> c17(A__TL(cons(z0, tl(adx(0))))) MARK(hd(adx(adx(y0)))) -> c16(MARK(adx(adx(y0)))) MARK(hd(adx(incr(y0)))) -> c16(MARK(adx(incr(y0)))) MARK(hd(adx(hd(cons(y0, y1))))) -> c16(MARK(adx(hd(cons(y0, y1))))) MARK(hd(adx(tl(cons(y0, y1))))) -> c16(MARK(adx(tl(cons(y0, y1))))) MARK(hd(adx(hd(adx(nats))))) -> c16(MARK(adx(hd(adx(nats))))) MARK(hd(adx(hd(adx(adx(y0)))))) -> c16(MARK(adx(hd(adx(adx(y0)))))) MARK(hd(adx(hd(adx(zeros))))) -> c16(MARK(adx(hd(adx(zeros))))) MARK(hd(adx(hd(adx(incr(y0)))))) -> c16(MARK(adx(hd(adx(incr(y0)))))) MARK(hd(adx(hd(adx(hd(y0)))))) -> c16(MARK(adx(hd(adx(hd(y0)))))) MARK(hd(adx(hd(adx(tl(y0)))))) -> c16(MARK(adx(hd(adx(tl(y0)))))) MARK(hd(adx(hd(adx(cons(y0, y1)))))) -> c16(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(hd(adx(hd(adx(y0))))) -> c16(MARK(adx(hd(adx(y0))))) MARK(hd(adx(hd(incr(nats))))) -> c16(MARK(adx(hd(incr(nats))))) MARK(hd(adx(hd(incr(adx(y0)))))) -> c16(MARK(adx(hd(incr(adx(y0)))))) MARK(hd(adx(hd(incr(zeros))))) -> c16(MARK(adx(hd(incr(zeros))))) MARK(hd(adx(hd(incr(incr(y0)))))) -> c16(MARK(adx(hd(incr(incr(y0)))))) MARK(hd(adx(hd(incr(hd(y0)))))) -> c16(MARK(adx(hd(incr(hd(y0)))))) MARK(hd(adx(hd(incr(tl(y0)))))) -> c16(MARK(adx(hd(incr(tl(y0)))))) MARK(hd(adx(hd(incr(cons(y0, y1)))))) -> c16(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(hd(adx(hd(incr(y0))))) -> c16(MARK(adx(hd(incr(y0))))) MARK(hd(adx(hd(hd(nats))))) -> c16(MARK(adx(hd(hd(nats))))) MARK(hd(adx(hd(hd(adx(y0)))))) -> c16(MARK(adx(hd(hd(adx(y0)))))) MARK(hd(adx(hd(hd(incr(y0)))))) -> c16(MARK(adx(hd(hd(incr(y0)))))) MARK(hd(adx(hd(hd(hd(y0)))))) -> c16(MARK(adx(hd(hd(hd(y0)))))) MARK(hd(adx(hd(hd(tl(y0)))))) -> c16(MARK(adx(hd(hd(tl(y0)))))) MARK(hd(adx(hd(hd(cons(y0, y1)))))) -> c16(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(hd(adx(hd(hd(y0))))) -> c16(MARK(adx(hd(hd(y0))))) MARK(hd(adx(hd(tl(nats))))) -> c16(MARK(adx(hd(tl(nats))))) MARK(hd(adx(hd(tl(adx(y0)))))) -> c16(MARK(adx(hd(tl(adx(y0)))))) MARK(hd(adx(hd(tl(incr(y0)))))) -> c16(MARK(adx(hd(tl(incr(y0)))))) MARK(hd(adx(hd(tl(hd(y0)))))) -> c16(MARK(adx(hd(tl(hd(y0)))))) MARK(hd(adx(hd(tl(tl(y0)))))) -> c16(MARK(adx(hd(tl(tl(y0)))))) MARK(hd(adx(hd(tl(cons(y0, y1)))))) -> c16(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(hd(adx(hd(tl(y0))))) -> c16(MARK(adx(hd(tl(y0))))) MARK(hd(adx(hd(nats)))) -> c16(MARK(adx(hd(nats)))) MARK(hd(adx(tl(adx(nats))))) -> c16(MARK(adx(tl(adx(nats))))) MARK(hd(adx(tl(adx(adx(y0)))))) -> c16(MARK(adx(tl(adx(adx(y0)))))) MARK(hd(adx(tl(adx(zeros))))) -> c16(MARK(adx(tl(adx(zeros))))) MARK(hd(adx(tl(adx(incr(y0)))))) -> c16(MARK(adx(tl(adx(incr(y0)))))) MARK(hd(adx(tl(adx(hd(y0)))))) -> c16(MARK(adx(tl(adx(hd(y0)))))) MARK(hd(adx(tl(adx(tl(y0)))))) -> c16(MARK(adx(tl(adx(tl(y0)))))) MARK(hd(adx(tl(adx(cons(y0, y1)))))) -> c16(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(hd(adx(tl(adx(y0))))) -> c16(MARK(adx(tl(adx(y0))))) MARK(hd(adx(tl(incr(nats))))) -> c16(MARK(adx(tl(incr(nats))))) MARK(hd(adx(tl(incr(adx(y0)))))) -> c16(MARK(adx(tl(incr(adx(y0)))))) MARK(hd(adx(tl(incr(zeros))))) -> c16(MARK(adx(tl(incr(zeros))))) MARK(hd(adx(tl(incr(incr(y0)))))) -> c16(MARK(adx(tl(incr(incr(y0)))))) MARK(hd(adx(tl(incr(hd(y0)))))) -> c16(MARK(adx(tl(incr(hd(y0)))))) MARK(hd(adx(tl(incr(tl(y0)))))) -> c16(MARK(adx(tl(incr(tl(y0)))))) MARK(hd(adx(tl(incr(cons(y0, y1)))))) -> c16(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(hd(adx(tl(incr(s(y0)))))) -> c16(MARK(adx(tl(incr(s(y0)))))) MARK(hd(adx(tl(incr(y0))))) -> c16(MARK(adx(tl(incr(y0))))) MARK(hd(adx(tl(hd(nats))))) -> c16(MARK(adx(tl(hd(nats))))) MARK(hd(adx(tl(hd(adx(y0)))))) -> c16(MARK(adx(tl(hd(adx(y0)))))) MARK(hd(adx(tl(hd(incr(y0)))))) -> c16(MARK(adx(tl(hd(incr(y0)))))) MARK(hd(adx(tl(hd(hd(y0)))))) -> c16(MARK(adx(tl(hd(hd(y0)))))) MARK(hd(adx(tl(hd(tl(y0)))))) -> c16(MARK(adx(tl(hd(tl(y0)))))) MARK(hd(adx(tl(hd(cons(y0, y1)))))) -> c16(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(hd(adx(tl(hd(y0))))) -> c16(MARK(adx(tl(hd(y0))))) MARK(hd(adx(tl(tl(nats))))) -> c16(MARK(adx(tl(tl(nats))))) MARK(hd(adx(tl(tl(adx(y0)))))) -> c16(MARK(adx(tl(tl(adx(y0)))))) MARK(hd(adx(tl(tl(incr(y0)))))) -> c16(MARK(adx(tl(tl(incr(y0)))))) MARK(hd(adx(tl(tl(hd(y0)))))) -> c16(MARK(adx(tl(tl(hd(y0)))))) MARK(hd(adx(tl(tl(tl(y0)))))) -> c16(MARK(adx(tl(tl(tl(y0)))))) MARK(hd(adx(tl(tl(cons(y0, y1)))))) -> c16(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(hd(adx(tl(tl(y0))))) -> c16(MARK(adx(tl(tl(y0))))) MARK(hd(adx(tl(nats)))) -> c16(MARK(adx(tl(nats)))) MARK(hd(adx(hd(adx(0))))) -> c16(MARK(adx(hd(adx(0))))) MARK(hd(adx(hd(adx(s(y0)))))) -> c16(MARK(adx(hd(adx(s(y0)))))) MARK(hd(adx(hd(incr(0))))) -> c16(MARK(adx(hd(incr(0))))) MARK(hd(adx(hd(incr(s(y0)))))) -> c16(MARK(adx(hd(incr(s(y0)))))) MARK(hd(adx(hd(hd(zeros))))) -> c16(MARK(adx(hd(hd(zeros))))) MARK(hd(adx(tl(hd(zeros))))) -> c16(MARK(adx(tl(hd(zeros))))) MARK(hd(adx(tl(adx(0))))) -> c16(MARK(adx(tl(adx(0))))) MARK(hd(adx(hd(tl(zeros))))) -> c16(MARK(adx(hd(tl(zeros))))) MARK(hd(adx(tl(tl(zeros))))) -> c16(MARK(adx(tl(tl(zeros))))) MARK(hd(adx(tl(adx(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) MARK(hd(adx(tl(incr(0))))) -> c16(MARK(adx(tl(incr(0))))) S tuples: MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) MARK(tl(cons(z0, adx(y1)))) -> c17(A__TL(cons(z0, adx(y1)))) MARK(tl(cons(z0, incr(y1)))) -> c17(A__TL(cons(z0, incr(y1)))) MARK(tl(cons(z0, hd(cons(y1, y2))))) -> c17(A__TL(cons(z0, hd(cons(y1, y2))))) MARK(tl(cons(z0, tl(cons(y1, y2))))) -> c17(A__TL(cons(z0, tl(cons(y1, y2))))) MARK(tl(cons(z0, hd(adx(nats))))) -> c17(A__TL(cons(z0, hd(adx(nats))))) MARK(tl(cons(z0, hd(adx(adx(y1)))))) -> c17(A__TL(cons(z0, hd(adx(adx(y1)))))) MARK(tl(cons(z0, hd(adx(zeros))))) -> c17(A__TL(cons(z0, hd(adx(zeros))))) MARK(tl(cons(z0, hd(adx(incr(y1)))))) -> c17(A__TL(cons(z0, hd(adx(incr(y1)))))) MARK(tl(cons(z0, hd(adx(hd(y1)))))) -> c17(A__TL(cons(z0, hd(adx(hd(y1)))))) MARK(tl(cons(z0, hd(adx(tl(y1)))))) -> c17(A__TL(cons(z0, hd(adx(tl(y1)))))) MARK(tl(cons(z0, hd(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(adx(cons(y1, y2)))))) MARK(tl(cons(z0, hd(adx(y1))))) -> c17(A__TL(cons(z0, hd(adx(y1))))) MARK(tl(cons(z0, hd(incr(nats))))) -> c17(A__TL(cons(z0, hd(incr(nats))))) MARK(tl(cons(z0, hd(incr(adx(y1)))))) -> c17(A__TL(cons(z0, hd(incr(adx(y1)))))) MARK(tl(cons(z0, hd(incr(zeros))))) -> c17(A__TL(cons(z0, hd(incr(zeros))))) MARK(tl(cons(z0, hd(incr(incr(y1)))))) -> c17(A__TL(cons(z0, hd(incr(incr(y1)))))) MARK(tl(cons(z0, hd(incr(hd(y1)))))) -> c17(A__TL(cons(z0, hd(incr(hd(y1)))))) MARK(tl(cons(z0, hd(incr(tl(y1)))))) -> c17(A__TL(cons(z0, hd(incr(tl(y1)))))) MARK(tl(cons(z0, hd(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(incr(cons(y1, y2)))))) MARK(tl(cons(z0, hd(incr(y1))))) -> c17(A__TL(cons(z0, hd(incr(y1))))) MARK(tl(cons(z0, hd(hd(nats))))) -> c17(A__TL(cons(z0, hd(hd(nats))))) MARK(tl(cons(z0, hd(hd(adx(y1)))))) -> c17(A__TL(cons(z0, hd(hd(adx(y1)))))) MARK(tl(cons(z0, hd(hd(incr(y1)))))) -> c17(A__TL(cons(z0, hd(hd(incr(y1)))))) MARK(tl(cons(z0, hd(hd(hd(y1)))))) -> c17(A__TL(cons(z0, hd(hd(hd(y1)))))) MARK(tl(cons(z0, hd(hd(tl(y1)))))) -> c17(A__TL(cons(z0, hd(hd(tl(y1)))))) MARK(tl(cons(z0, hd(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(hd(cons(y1, y2)))))) MARK(tl(cons(z0, hd(hd(y1))))) -> c17(A__TL(cons(z0, hd(hd(y1))))) MARK(tl(cons(z0, hd(tl(nats))))) -> c17(A__TL(cons(z0, hd(tl(nats))))) MARK(tl(cons(z0, hd(tl(adx(y1)))))) -> c17(A__TL(cons(z0, hd(tl(adx(y1)))))) MARK(tl(cons(z0, hd(tl(zeros))))) -> c17(A__TL(cons(z0, hd(tl(zeros))))) MARK(tl(cons(z0, hd(tl(incr(y1)))))) -> c17(A__TL(cons(z0, hd(tl(incr(y1)))))) MARK(tl(cons(z0, hd(tl(hd(y1)))))) -> c17(A__TL(cons(z0, hd(tl(hd(y1)))))) MARK(tl(cons(z0, hd(tl(tl(y1)))))) -> c17(A__TL(cons(z0, hd(tl(tl(y1)))))) MARK(tl(cons(z0, hd(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(tl(cons(y1, y2)))))) MARK(tl(cons(z0, hd(tl(y1))))) -> c17(A__TL(cons(z0, hd(tl(y1))))) MARK(tl(cons(z0, hd(nats)))) -> c17(A__TL(cons(z0, hd(nats)))) MARK(tl(cons(z0, tl(adx(nats))))) -> c17(A__TL(cons(z0, tl(adx(nats))))) MARK(tl(cons(z0, tl(adx(adx(y1)))))) -> c17(A__TL(cons(z0, tl(adx(adx(y1)))))) MARK(tl(cons(z0, tl(adx(zeros))))) -> c17(A__TL(cons(z0, tl(adx(zeros))))) MARK(tl(cons(z0, tl(adx(incr(y1)))))) -> c17(A__TL(cons(z0, tl(adx(incr(y1)))))) MARK(tl(cons(z0, tl(adx(hd(y1)))))) -> c17(A__TL(cons(z0, tl(adx(hd(y1)))))) MARK(tl(cons(z0, tl(adx(tl(y1)))))) -> c17(A__TL(cons(z0, tl(adx(tl(y1)))))) MARK(tl(cons(z0, tl(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(adx(cons(y1, y2)))))) MARK(tl(cons(z0, tl(adx(s(y1)))))) -> c17(A__TL(cons(z0, tl(adx(s(y1)))))) MARK(tl(cons(z0, tl(adx(y1))))) -> c17(A__TL(cons(z0, tl(adx(y1))))) MARK(tl(cons(z0, tl(incr(nats))))) -> c17(A__TL(cons(z0, tl(incr(nats))))) MARK(tl(cons(z0, tl(incr(adx(y1)))))) -> c17(A__TL(cons(z0, tl(incr(adx(y1)))))) MARK(tl(cons(z0, tl(incr(zeros))))) -> c17(A__TL(cons(z0, tl(incr(zeros))))) MARK(tl(cons(z0, tl(incr(incr(y1)))))) -> c17(A__TL(cons(z0, tl(incr(incr(y1)))))) MARK(tl(cons(z0, tl(incr(hd(y1)))))) -> c17(A__TL(cons(z0, tl(incr(hd(y1)))))) MARK(tl(cons(z0, tl(incr(tl(y1)))))) -> c17(A__TL(cons(z0, tl(incr(tl(y1)))))) MARK(tl(cons(z0, tl(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(incr(cons(y1, y2)))))) MARK(tl(cons(z0, tl(incr(0))))) -> c17(A__TL(cons(z0, tl(incr(0))))) MARK(tl(cons(z0, tl(incr(s(y1)))))) -> c17(A__TL(cons(z0, tl(incr(s(y1)))))) MARK(tl(cons(z0, tl(incr(y1))))) -> c17(A__TL(cons(z0, tl(incr(y1))))) MARK(tl(cons(z0, tl(hd(nats))))) -> c17(A__TL(cons(z0, tl(hd(nats))))) MARK(tl(cons(z0, tl(hd(adx(y1)))))) -> c17(A__TL(cons(z0, tl(hd(adx(y1)))))) MARK(tl(cons(z0, tl(hd(incr(y1)))))) -> c17(A__TL(cons(z0, tl(hd(incr(y1)))))) MARK(tl(cons(z0, tl(hd(hd(y1)))))) -> c17(A__TL(cons(z0, tl(hd(hd(y1)))))) MARK(tl(cons(z0, tl(hd(tl(y1)))))) -> c17(A__TL(cons(z0, tl(hd(tl(y1)))))) MARK(tl(cons(z0, tl(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(hd(cons(y1, y2)))))) MARK(tl(cons(z0, tl(hd(y1))))) -> c17(A__TL(cons(z0, tl(hd(y1))))) MARK(tl(cons(z0, tl(tl(nats))))) -> c17(A__TL(cons(z0, tl(tl(nats))))) MARK(tl(cons(z0, tl(tl(adx(y1)))))) -> c17(A__TL(cons(z0, tl(tl(adx(y1)))))) MARK(tl(cons(z0, tl(tl(zeros))))) -> c17(A__TL(cons(z0, tl(tl(zeros))))) MARK(tl(cons(z0, tl(tl(incr(y1)))))) -> c17(A__TL(cons(z0, tl(tl(incr(y1)))))) MARK(tl(cons(z0, tl(tl(hd(y1)))))) -> c17(A__TL(cons(z0, tl(tl(hd(y1)))))) MARK(tl(cons(z0, tl(tl(tl(y1)))))) -> c17(A__TL(cons(z0, tl(tl(tl(y1)))))) MARK(tl(cons(z0, tl(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(tl(cons(y1, y2)))))) MARK(tl(cons(z0, tl(tl(y1))))) -> c17(A__TL(cons(z0, tl(tl(y1))))) MARK(tl(cons(z0, tl(nats)))) -> c17(A__TL(cons(z0, tl(nats)))) MARK(tl(cons(z0, hd(adx(0))))) -> c17(A__TL(cons(z0, hd(adx(0))))) MARK(tl(cons(z0, hd(adx(s(y1)))))) -> c17(A__TL(cons(z0, hd(adx(s(y1)))))) MARK(tl(cons(z0, hd(incr(0))))) -> c17(A__TL(cons(z0, hd(incr(0))))) MARK(tl(cons(z0, hd(incr(s(y1)))))) -> c17(A__TL(cons(z0, hd(incr(s(y1)))))) MARK(tl(cons(z0, hd(hd(zeros))))) -> c17(A__TL(cons(z0, hd(hd(zeros))))) MARK(tl(cons(z0, tl(hd(zeros))))) -> c17(A__TL(cons(z0, tl(hd(zeros))))) MARK(tl(cons(z0, tl(adx(0))))) -> c17(A__TL(cons(z0, tl(adx(0))))) MARK(hd(adx(adx(y0)))) -> c16(MARK(adx(adx(y0)))) MARK(hd(adx(incr(y0)))) -> c16(MARK(adx(incr(y0)))) MARK(hd(adx(hd(cons(y0, y1))))) -> c16(MARK(adx(hd(cons(y0, y1))))) MARK(hd(adx(tl(cons(y0, y1))))) -> c16(MARK(adx(tl(cons(y0, y1))))) MARK(hd(adx(hd(adx(nats))))) -> c16(MARK(adx(hd(adx(nats))))) MARK(hd(adx(hd(adx(adx(y0)))))) -> c16(MARK(adx(hd(adx(adx(y0)))))) MARK(hd(adx(hd(adx(zeros))))) -> c16(MARK(adx(hd(adx(zeros))))) MARK(hd(adx(hd(adx(incr(y0)))))) -> c16(MARK(adx(hd(adx(incr(y0)))))) MARK(hd(adx(hd(adx(hd(y0)))))) -> c16(MARK(adx(hd(adx(hd(y0)))))) MARK(hd(adx(hd(adx(tl(y0)))))) -> c16(MARK(adx(hd(adx(tl(y0)))))) MARK(hd(adx(hd(adx(cons(y0, y1)))))) -> c16(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(hd(adx(hd(adx(y0))))) -> c16(MARK(adx(hd(adx(y0))))) MARK(hd(adx(hd(incr(nats))))) -> c16(MARK(adx(hd(incr(nats))))) MARK(hd(adx(hd(incr(adx(y0)))))) -> c16(MARK(adx(hd(incr(adx(y0)))))) MARK(hd(adx(hd(incr(zeros))))) -> c16(MARK(adx(hd(incr(zeros))))) MARK(hd(adx(hd(incr(incr(y0)))))) -> c16(MARK(adx(hd(incr(incr(y0)))))) MARK(hd(adx(hd(incr(hd(y0)))))) -> c16(MARK(adx(hd(incr(hd(y0)))))) MARK(hd(adx(hd(incr(tl(y0)))))) -> c16(MARK(adx(hd(incr(tl(y0)))))) MARK(hd(adx(hd(incr(cons(y0, y1)))))) -> c16(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(hd(adx(hd(incr(y0))))) -> c16(MARK(adx(hd(incr(y0))))) MARK(hd(adx(hd(hd(nats))))) -> c16(MARK(adx(hd(hd(nats))))) MARK(hd(adx(hd(hd(adx(y0)))))) -> c16(MARK(adx(hd(hd(adx(y0)))))) MARK(hd(adx(hd(hd(incr(y0)))))) -> c16(MARK(adx(hd(hd(incr(y0)))))) MARK(hd(adx(hd(hd(hd(y0)))))) -> c16(MARK(adx(hd(hd(hd(y0)))))) MARK(hd(adx(hd(hd(tl(y0)))))) -> c16(MARK(adx(hd(hd(tl(y0)))))) MARK(hd(adx(hd(hd(cons(y0, y1)))))) -> c16(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(hd(adx(hd(hd(y0))))) -> c16(MARK(adx(hd(hd(y0))))) MARK(hd(adx(hd(tl(nats))))) -> c16(MARK(adx(hd(tl(nats))))) MARK(hd(adx(hd(tl(adx(y0)))))) -> c16(MARK(adx(hd(tl(adx(y0)))))) MARK(hd(adx(hd(tl(incr(y0)))))) -> c16(MARK(adx(hd(tl(incr(y0)))))) MARK(hd(adx(hd(tl(hd(y0)))))) -> c16(MARK(adx(hd(tl(hd(y0)))))) MARK(hd(adx(hd(tl(tl(y0)))))) -> c16(MARK(adx(hd(tl(tl(y0)))))) MARK(hd(adx(hd(tl(cons(y0, y1)))))) -> c16(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(hd(adx(hd(tl(y0))))) -> c16(MARK(adx(hd(tl(y0))))) MARK(hd(adx(hd(nats)))) -> c16(MARK(adx(hd(nats)))) MARK(hd(adx(tl(adx(nats))))) -> c16(MARK(adx(tl(adx(nats))))) MARK(hd(adx(tl(adx(adx(y0)))))) -> c16(MARK(adx(tl(adx(adx(y0)))))) MARK(hd(adx(tl(adx(zeros))))) -> c16(MARK(adx(tl(adx(zeros))))) MARK(hd(adx(tl(adx(incr(y0)))))) -> c16(MARK(adx(tl(adx(incr(y0)))))) MARK(hd(adx(tl(adx(hd(y0)))))) -> c16(MARK(adx(tl(adx(hd(y0)))))) MARK(hd(adx(tl(adx(tl(y0)))))) -> c16(MARK(adx(tl(adx(tl(y0)))))) MARK(hd(adx(tl(adx(cons(y0, y1)))))) -> c16(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(hd(adx(tl(adx(y0))))) -> c16(MARK(adx(tl(adx(y0))))) MARK(hd(adx(tl(incr(nats))))) -> c16(MARK(adx(tl(incr(nats))))) MARK(hd(adx(tl(incr(adx(y0)))))) -> c16(MARK(adx(tl(incr(adx(y0)))))) MARK(hd(adx(tl(incr(zeros))))) -> c16(MARK(adx(tl(incr(zeros))))) MARK(hd(adx(tl(incr(incr(y0)))))) -> c16(MARK(adx(tl(incr(incr(y0)))))) MARK(hd(adx(tl(incr(hd(y0)))))) -> c16(MARK(adx(tl(incr(hd(y0)))))) MARK(hd(adx(tl(incr(tl(y0)))))) -> c16(MARK(adx(tl(incr(tl(y0)))))) MARK(hd(adx(tl(incr(cons(y0, y1)))))) -> c16(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(hd(adx(tl(incr(s(y0)))))) -> c16(MARK(adx(tl(incr(s(y0)))))) MARK(hd(adx(tl(incr(y0))))) -> c16(MARK(adx(tl(incr(y0))))) MARK(hd(adx(tl(hd(nats))))) -> c16(MARK(adx(tl(hd(nats))))) MARK(hd(adx(tl(hd(adx(y0)))))) -> c16(MARK(adx(tl(hd(adx(y0)))))) MARK(hd(adx(tl(hd(incr(y0)))))) -> c16(MARK(adx(tl(hd(incr(y0)))))) MARK(hd(adx(tl(hd(hd(y0)))))) -> c16(MARK(adx(tl(hd(hd(y0)))))) MARK(hd(adx(tl(hd(tl(y0)))))) -> c16(MARK(adx(tl(hd(tl(y0)))))) MARK(hd(adx(tl(hd(cons(y0, y1)))))) -> c16(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(hd(adx(tl(hd(y0))))) -> c16(MARK(adx(tl(hd(y0))))) MARK(hd(adx(tl(tl(nats))))) -> c16(MARK(adx(tl(tl(nats))))) MARK(hd(adx(tl(tl(adx(y0)))))) -> c16(MARK(adx(tl(tl(adx(y0)))))) MARK(hd(adx(tl(tl(incr(y0)))))) -> c16(MARK(adx(tl(tl(incr(y0)))))) MARK(hd(adx(tl(tl(hd(y0)))))) -> c16(MARK(adx(tl(tl(hd(y0)))))) MARK(hd(adx(tl(tl(tl(y0)))))) -> c16(MARK(adx(tl(tl(tl(y0)))))) MARK(hd(adx(tl(tl(cons(y0, y1)))))) -> c16(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(hd(adx(tl(tl(y0))))) -> c16(MARK(adx(tl(tl(y0))))) MARK(hd(adx(tl(nats)))) -> c16(MARK(adx(tl(nats)))) MARK(hd(adx(hd(adx(0))))) -> c16(MARK(adx(hd(adx(0))))) MARK(hd(adx(hd(adx(s(y0)))))) -> c16(MARK(adx(hd(adx(s(y0)))))) MARK(hd(adx(hd(incr(0))))) -> c16(MARK(adx(hd(incr(0))))) MARK(hd(adx(hd(incr(s(y0)))))) -> c16(MARK(adx(hd(incr(s(y0)))))) MARK(hd(adx(hd(hd(zeros))))) -> c16(MARK(adx(hd(hd(zeros))))) MARK(hd(adx(tl(hd(zeros))))) -> c16(MARK(adx(tl(hd(zeros))))) MARK(hd(adx(tl(adx(0))))) -> c16(MARK(adx(tl(adx(0))))) MARK(hd(adx(hd(tl(zeros))))) -> c16(MARK(adx(hd(tl(zeros))))) MARK(hd(adx(tl(tl(zeros))))) -> c16(MARK(adx(tl(tl(zeros))))) MARK(hd(adx(tl(adx(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) MARK(hd(adx(tl(incr(0))))) -> c16(MARK(adx(tl(incr(0))))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c16_2, c16_1, c17_2, c17_1, c8_1, c10_1, c13_1, c15_1 ---------------------------------------- (205) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing nodes: A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, 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A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) MARK(tl(cons(z0, adx(y1)))) -> c17(A__TL(cons(z0, adx(y1)))) MARK(tl(cons(z0, incr(y1)))) -> c17(A__TL(cons(z0, incr(y1)))) MARK(tl(cons(z0, hd(cons(y1, y2))))) -> c17(A__TL(cons(z0, hd(cons(y1, y2))))) MARK(tl(cons(z0, tl(cons(y1, y2))))) -> c17(A__TL(cons(z0, tl(cons(y1, y2))))) MARK(tl(cons(z0, hd(adx(nats))))) -> c17(A__TL(cons(z0, hd(adx(nats))))) MARK(tl(cons(z0, hd(adx(adx(y1)))))) -> c17(A__TL(cons(z0, hd(adx(adx(y1)))))) MARK(tl(cons(z0, hd(adx(zeros))))) -> c17(A__TL(cons(z0, hd(adx(zeros))))) MARK(tl(cons(z0, hd(adx(incr(y1)))))) -> c17(A__TL(cons(z0, hd(adx(incr(y1)))))) MARK(tl(cons(z0, hd(adx(hd(y1)))))) -> c17(A__TL(cons(z0, hd(adx(hd(y1)))))) MARK(tl(cons(z0, hd(adx(tl(y1)))))) -> c17(A__TL(cons(z0, hd(adx(tl(y1)))))) MARK(tl(cons(z0, hd(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(adx(cons(y1, y2)))))) MARK(tl(cons(z0, hd(adx(y1))))) -> c17(A__TL(cons(z0, hd(adx(y1))))) MARK(tl(cons(z0, hd(incr(nats))))) -> c17(A__TL(cons(z0, hd(incr(nats))))) MARK(tl(cons(z0, hd(incr(adx(y1)))))) -> c17(A__TL(cons(z0, hd(incr(adx(y1)))))) MARK(tl(cons(z0, hd(incr(zeros))))) -> c17(A__TL(cons(z0, hd(incr(zeros))))) MARK(tl(cons(z0, hd(incr(incr(y1)))))) -> c17(A__TL(cons(z0, hd(incr(incr(y1)))))) MARK(tl(cons(z0, hd(incr(hd(y1)))))) -> c17(A__TL(cons(z0, hd(incr(hd(y1)))))) MARK(tl(cons(z0, hd(incr(tl(y1)))))) -> c17(A__TL(cons(z0, hd(incr(tl(y1)))))) MARK(tl(cons(z0, hd(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(incr(cons(y1, y2)))))) MARK(tl(cons(z0, hd(incr(y1))))) -> c17(A__TL(cons(z0, hd(incr(y1))))) MARK(tl(cons(z0, hd(hd(nats))))) -> c17(A__TL(cons(z0, hd(hd(nats))))) MARK(tl(cons(z0, hd(hd(adx(y1)))))) -> c17(A__TL(cons(z0, hd(hd(adx(y1)))))) MARK(tl(cons(z0, hd(hd(incr(y1)))))) -> c17(A__TL(cons(z0, hd(hd(incr(y1)))))) MARK(tl(cons(z0, hd(hd(hd(y1)))))) -> c17(A__TL(cons(z0, hd(hd(hd(y1)))))) MARK(tl(cons(z0, hd(hd(tl(y1)))))) -> c17(A__TL(cons(z0, hd(hd(tl(y1)))))) MARK(tl(cons(z0, hd(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(hd(cons(y1, y2)))))) MARK(tl(cons(z0, hd(hd(y1))))) -> c17(A__TL(cons(z0, hd(hd(y1))))) MARK(tl(cons(z0, hd(tl(nats))))) -> c17(A__TL(cons(z0, hd(tl(nats))))) MARK(tl(cons(z0, hd(tl(adx(y1)))))) -> c17(A__TL(cons(z0, hd(tl(adx(y1)))))) MARK(tl(cons(z0, hd(tl(zeros))))) -> c17(A__TL(cons(z0, hd(tl(zeros))))) MARK(tl(cons(z0, hd(tl(incr(y1)))))) -> c17(A__TL(cons(z0, hd(tl(incr(y1)))))) MARK(tl(cons(z0, hd(tl(hd(y1)))))) -> c17(A__TL(cons(z0, hd(tl(hd(y1)))))) MARK(tl(cons(z0, hd(tl(tl(y1)))))) -> c17(A__TL(cons(z0, hd(tl(tl(y1)))))) MARK(tl(cons(z0, hd(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(tl(cons(y1, y2)))))) MARK(tl(cons(z0, hd(tl(y1))))) -> c17(A__TL(cons(z0, hd(tl(y1))))) MARK(tl(cons(z0, hd(nats)))) -> c17(A__TL(cons(z0, hd(nats)))) MARK(tl(cons(z0, tl(adx(nats))))) -> c17(A__TL(cons(z0, tl(adx(nats))))) MARK(tl(cons(z0, tl(adx(adx(y1)))))) -> c17(A__TL(cons(z0, tl(adx(adx(y1)))))) MARK(tl(cons(z0, tl(adx(zeros))))) -> c17(A__TL(cons(z0, tl(adx(zeros))))) MARK(tl(cons(z0, tl(adx(incr(y1)))))) -> c17(A__TL(cons(z0, tl(adx(incr(y1)))))) MARK(tl(cons(z0, tl(adx(hd(y1)))))) -> c17(A__TL(cons(z0, tl(adx(hd(y1)))))) MARK(tl(cons(z0, tl(adx(tl(y1)))))) -> c17(A__TL(cons(z0, tl(adx(tl(y1)))))) MARK(tl(cons(z0, tl(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(adx(cons(y1, y2)))))) MARK(tl(cons(z0, tl(adx(s(y1)))))) -> c17(A__TL(cons(z0, tl(adx(s(y1)))))) MARK(tl(cons(z0, tl(adx(y1))))) -> c17(A__TL(cons(z0, tl(adx(y1))))) MARK(tl(cons(z0, tl(incr(nats))))) -> c17(A__TL(cons(z0, tl(incr(nats))))) MARK(tl(cons(z0, tl(incr(adx(y1)))))) -> c17(A__TL(cons(z0, tl(incr(adx(y1)))))) MARK(tl(cons(z0, tl(incr(zeros))))) -> c17(A__TL(cons(z0, tl(incr(zeros))))) MARK(tl(cons(z0, tl(incr(incr(y1)))))) -> c17(A__TL(cons(z0, tl(incr(incr(y1)))))) MARK(tl(cons(z0, tl(incr(hd(y1)))))) -> c17(A__TL(cons(z0, tl(incr(hd(y1)))))) MARK(tl(cons(z0, tl(incr(tl(y1)))))) -> c17(A__TL(cons(z0, tl(incr(tl(y1)))))) MARK(tl(cons(z0, tl(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(incr(cons(y1, y2)))))) MARK(tl(cons(z0, tl(incr(0))))) -> c17(A__TL(cons(z0, tl(incr(0))))) MARK(tl(cons(z0, tl(incr(s(y1)))))) -> c17(A__TL(cons(z0, tl(incr(s(y1)))))) MARK(tl(cons(z0, tl(incr(y1))))) -> c17(A__TL(cons(z0, tl(incr(y1))))) MARK(tl(cons(z0, tl(hd(nats))))) -> c17(A__TL(cons(z0, tl(hd(nats))))) MARK(tl(cons(z0, tl(hd(adx(y1)))))) -> c17(A__TL(cons(z0, tl(hd(adx(y1)))))) MARK(tl(cons(z0, tl(hd(incr(y1)))))) -> c17(A__TL(cons(z0, tl(hd(incr(y1)))))) MARK(tl(cons(z0, tl(hd(hd(y1)))))) -> c17(A__TL(cons(z0, tl(hd(hd(y1)))))) MARK(tl(cons(z0, tl(hd(tl(y1)))))) -> c17(A__TL(cons(z0, tl(hd(tl(y1)))))) MARK(tl(cons(z0, tl(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(hd(cons(y1, y2)))))) MARK(tl(cons(z0, tl(hd(y1))))) -> c17(A__TL(cons(z0, tl(hd(y1))))) MARK(tl(cons(z0, tl(tl(nats))))) -> c17(A__TL(cons(z0, tl(tl(nats))))) MARK(tl(cons(z0, tl(tl(adx(y1)))))) -> c17(A__TL(cons(z0, tl(tl(adx(y1)))))) MARK(tl(cons(z0, tl(tl(zeros))))) -> c17(A__TL(cons(z0, tl(tl(zeros))))) MARK(tl(cons(z0, tl(tl(incr(y1)))))) -> c17(A__TL(cons(z0, tl(tl(incr(y1)))))) MARK(tl(cons(z0, tl(tl(hd(y1)))))) -> c17(A__TL(cons(z0, tl(tl(hd(y1)))))) MARK(tl(cons(z0, tl(tl(tl(y1)))))) -> c17(A__TL(cons(z0, tl(tl(tl(y1)))))) MARK(tl(cons(z0, tl(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(tl(cons(y1, y2)))))) MARK(tl(cons(z0, tl(tl(y1))))) -> c17(A__TL(cons(z0, tl(tl(y1))))) MARK(tl(cons(z0, tl(nats)))) -> c17(A__TL(cons(z0, tl(nats)))) MARK(tl(cons(z0, hd(adx(0))))) -> c17(A__TL(cons(z0, hd(adx(0))))) MARK(tl(cons(z0, hd(adx(s(y1)))))) -> c17(A__TL(cons(z0, hd(adx(s(y1)))))) MARK(tl(cons(z0, hd(incr(0))))) -> c17(A__TL(cons(z0, hd(incr(0))))) MARK(tl(cons(z0, hd(incr(s(y1)))))) -> c17(A__TL(cons(z0, hd(incr(s(y1)))))) MARK(tl(cons(z0, hd(hd(zeros))))) -> c17(A__TL(cons(z0, hd(hd(zeros))))) MARK(tl(cons(z0, tl(hd(zeros))))) -> c17(A__TL(cons(z0, tl(hd(zeros))))) MARK(tl(cons(z0, tl(adx(0))))) -> c17(A__TL(cons(z0, tl(adx(0))))) MARK(hd(adx(adx(y0)))) -> c16(MARK(adx(adx(y0)))) MARK(hd(adx(incr(y0)))) -> c16(MARK(adx(incr(y0)))) MARK(hd(adx(hd(cons(y0, y1))))) -> c16(MARK(adx(hd(cons(y0, y1))))) MARK(hd(adx(tl(cons(y0, y1))))) -> c16(MARK(adx(tl(cons(y0, y1))))) MARK(hd(adx(hd(adx(nats))))) -> c16(MARK(adx(hd(adx(nats))))) MARK(hd(adx(hd(adx(adx(y0)))))) -> c16(MARK(adx(hd(adx(adx(y0)))))) MARK(hd(adx(hd(adx(zeros))))) -> c16(MARK(adx(hd(adx(zeros))))) MARK(hd(adx(hd(adx(incr(y0)))))) -> c16(MARK(adx(hd(adx(incr(y0)))))) MARK(hd(adx(hd(adx(hd(y0)))))) -> c16(MARK(adx(hd(adx(hd(y0)))))) MARK(hd(adx(hd(adx(tl(y0)))))) -> c16(MARK(adx(hd(adx(tl(y0)))))) MARK(hd(adx(hd(adx(cons(y0, y1)))))) -> c16(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(hd(adx(hd(adx(y0))))) -> c16(MARK(adx(hd(adx(y0))))) MARK(hd(adx(hd(incr(nats))))) -> c16(MARK(adx(hd(incr(nats))))) MARK(hd(adx(hd(incr(adx(y0)))))) -> c16(MARK(adx(hd(incr(adx(y0)))))) MARK(hd(adx(hd(incr(zeros))))) -> c16(MARK(adx(hd(incr(zeros))))) MARK(hd(adx(hd(incr(incr(y0)))))) -> c16(MARK(adx(hd(incr(incr(y0)))))) MARK(hd(adx(hd(incr(hd(y0)))))) -> c16(MARK(adx(hd(incr(hd(y0)))))) MARK(hd(adx(hd(incr(tl(y0)))))) -> c16(MARK(adx(hd(incr(tl(y0)))))) MARK(hd(adx(hd(incr(cons(y0, y1)))))) -> c16(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(hd(adx(hd(incr(y0))))) -> c16(MARK(adx(hd(incr(y0))))) MARK(hd(adx(hd(hd(nats))))) -> c16(MARK(adx(hd(hd(nats))))) MARK(hd(adx(hd(hd(adx(y0)))))) -> c16(MARK(adx(hd(hd(adx(y0)))))) MARK(hd(adx(hd(hd(incr(y0)))))) -> c16(MARK(adx(hd(hd(incr(y0)))))) MARK(hd(adx(hd(hd(hd(y0)))))) -> c16(MARK(adx(hd(hd(hd(y0)))))) MARK(hd(adx(hd(hd(tl(y0)))))) -> c16(MARK(adx(hd(hd(tl(y0)))))) MARK(hd(adx(hd(hd(cons(y0, y1)))))) -> c16(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(hd(adx(hd(hd(y0))))) -> c16(MARK(adx(hd(hd(y0))))) MARK(hd(adx(hd(tl(nats))))) -> c16(MARK(adx(hd(tl(nats))))) MARK(hd(adx(hd(tl(adx(y0)))))) -> c16(MARK(adx(hd(tl(adx(y0)))))) MARK(hd(adx(hd(tl(incr(y0)))))) -> c16(MARK(adx(hd(tl(incr(y0)))))) MARK(hd(adx(hd(tl(hd(y0)))))) -> c16(MARK(adx(hd(tl(hd(y0)))))) MARK(hd(adx(hd(tl(tl(y0)))))) -> c16(MARK(adx(hd(tl(tl(y0)))))) MARK(hd(adx(hd(tl(cons(y0, y1)))))) -> c16(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(hd(adx(hd(tl(y0))))) -> c16(MARK(adx(hd(tl(y0))))) MARK(hd(adx(hd(nats)))) -> c16(MARK(adx(hd(nats)))) MARK(hd(adx(tl(adx(nats))))) -> c16(MARK(adx(tl(adx(nats))))) MARK(hd(adx(tl(adx(adx(y0)))))) -> c16(MARK(adx(tl(adx(adx(y0)))))) MARK(hd(adx(tl(adx(zeros))))) -> c16(MARK(adx(tl(adx(zeros))))) MARK(hd(adx(tl(adx(incr(y0)))))) -> c16(MARK(adx(tl(adx(incr(y0)))))) MARK(hd(adx(tl(adx(hd(y0)))))) -> c16(MARK(adx(tl(adx(hd(y0)))))) MARK(hd(adx(tl(adx(tl(y0)))))) -> c16(MARK(adx(tl(adx(tl(y0)))))) MARK(hd(adx(tl(adx(cons(y0, y1)))))) -> c16(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(hd(adx(tl(adx(y0))))) -> c16(MARK(adx(tl(adx(y0))))) MARK(hd(adx(tl(incr(nats))))) -> c16(MARK(adx(tl(incr(nats))))) MARK(hd(adx(tl(incr(adx(y0)))))) -> c16(MARK(adx(tl(incr(adx(y0)))))) MARK(hd(adx(tl(incr(zeros))))) -> c16(MARK(adx(tl(incr(zeros))))) MARK(hd(adx(tl(incr(incr(y0)))))) -> c16(MARK(adx(tl(incr(incr(y0)))))) MARK(hd(adx(tl(incr(hd(y0)))))) -> c16(MARK(adx(tl(incr(hd(y0)))))) MARK(hd(adx(tl(incr(tl(y0)))))) -> c16(MARK(adx(tl(incr(tl(y0)))))) MARK(hd(adx(tl(incr(cons(y0, y1)))))) -> c16(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(hd(adx(tl(incr(s(y0)))))) -> c16(MARK(adx(tl(incr(s(y0)))))) MARK(hd(adx(tl(incr(y0))))) -> c16(MARK(adx(tl(incr(y0))))) MARK(hd(adx(tl(hd(nats))))) -> c16(MARK(adx(tl(hd(nats))))) MARK(hd(adx(tl(hd(adx(y0)))))) -> c16(MARK(adx(tl(hd(adx(y0)))))) MARK(hd(adx(tl(hd(incr(y0)))))) -> c16(MARK(adx(tl(hd(incr(y0)))))) MARK(hd(adx(tl(hd(hd(y0)))))) -> c16(MARK(adx(tl(hd(hd(y0)))))) MARK(hd(adx(tl(hd(tl(y0)))))) -> c16(MARK(adx(tl(hd(tl(y0)))))) MARK(hd(adx(tl(hd(cons(y0, y1)))))) -> c16(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(hd(adx(tl(hd(y0))))) -> c16(MARK(adx(tl(hd(y0))))) MARK(hd(adx(tl(tl(nats))))) -> c16(MARK(adx(tl(tl(nats))))) MARK(hd(adx(tl(tl(adx(y0)))))) -> c16(MARK(adx(tl(tl(adx(y0)))))) MARK(hd(adx(tl(tl(incr(y0)))))) -> c16(MARK(adx(tl(tl(incr(y0)))))) MARK(hd(adx(tl(tl(hd(y0)))))) -> c16(MARK(adx(tl(tl(hd(y0)))))) MARK(hd(adx(tl(tl(tl(y0)))))) -> c16(MARK(adx(tl(tl(tl(y0)))))) MARK(hd(adx(tl(tl(cons(y0, y1)))))) -> c16(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(hd(adx(tl(tl(y0))))) -> c16(MARK(adx(tl(tl(y0))))) MARK(hd(adx(tl(nats)))) -> c16(MARK(adx(tl(nats)))) MARK(hd(adx(hd(adx(0))))) -> c16(MARK(adx(hd(adx(0))))) MARK(hd(adx(hd(adx(s(y0)))))) -> c16(MARK(adx(hd(adx(s(y0)))))) MARK(hd(adx(hd(incr(0))))) -> c16(MARK(adx(hd(incr(0))))) MARK(hd(adx(hd(incr(s(y0)))))) -> c16(MARK(adx(hd(incr(s(y0)))))) MARK(hd(adx(hd(hd(zeros))))) -> c16(MARK(adx(hd(hd(zeros))))) MARK(hd(adx(tl(hd(zeros))))) -> c16(MARK(adx(tl(hd(zeros))))) MARK(hd(adx(tl(adx(0))))) -> c16(MARK(adx(tl(adx(0))))) MARK(hd(adx(hd(tl(zeros))))) -> c16(MARK(adx(hd(tl(zeros))))) MARK(hd(adx(tl(tl(zeros))))) -> c16(MARK(adx(tl(tl(zeros))))) MARK(hd(adx(tl(adx(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) MARK(hd(adx(tl(incr(0))))) -> c16(MARK(adx(tl(incr(0))))) S tuples: MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, 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tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) MARK(tl(cons(z0, adx(y1)))) -> c17(A__TL(cons(z0, adx(y1)))) MARK(tl(cons(z0, incr(y1)))) -> c17(A__TL(cons(z0, incr(y1)))) MARK(tl(cons(z0, hd(cons(y1, y2))))) -> c17(A__TL(cons(z0, hd(cons(y1, y2))))) MARK(tl(cons(z0, tl(cons(y1, y2))))) -> c17(A__TL(cons(z0, tl(cons(y1, y2))))) MARK(tl(cons(z0, hd(adx(nats))))) -> c17(A__TL(cons(z0, hd(adx(nats))))) MARK(tl(cons(z0, hd(adx(adx(y1)))))) -> c17(A__TL(cons(z0, hd(adx(adx(y1)))))) MARK(tl(cons(z0, hd(adx(zeros))))) -> c17(A__TL(cons(z0, hd(adx(zeros))))) MARK(tl(cons(z0, hd(adx(incr(y1)))))) -> c17(A__TL(cons(z0, hd(adx(incr(y1)))))) MARK(tl(cons(z0, hd(adx(hd(y1)))))) -> c17(A__TL(cons(z0, hd(adx(hd(y1)))))) MARK(tl(cons(z0, hd(adx(tl(y1)))))) -> c17(A__TL(cons(z0, hd(adx(tl(y1)))))) MARK(tl(cons(z0, hd(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(adx(cons(y1, y2)))))) MARK(tl(cons(z0, hd(adx(y1))))) -> c17(A__TL(cons(z0, hd(adx(y1))))) MARK(tl(cons(z0, hd(incr(nats))))) -> c17(A__TL(cons(z0, hd(incr(nats))))) MARK(tl(cons(z0, hd(incr(adx(y1)))))) -> c17(A__TL(cons(z0, hd(incr(adx(y1)))))) MARK(tl(cons(z0, hd(incr(zeros))))) -> c17(A__TL(cons(z0, hd(incr(zeros))))) MARK(tl(cons(z0, hd(incr(incr(y1)))))) -> c17(A__TL(cons(z0, hd(incr(incr(y1)))))) MARK(tl(cons(z0, hd(incr(hd(y1)))))) -> c17(A__TL(cons(z0, hd(incr(hd(y1)))))) MARK(tl(cons(z0, hd(incr(tl(y1)))))) -> c17(A__TL(cons(z0, hd(incr(tl(y1)))))) MARK(tl(cons(z0, hd(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(incr(cons(y1, y2)))))) MARK(tl(cons(z0, hd(incr(y1))))) -> c17(A__TL(cons(z0, hd(incr(y1))))) MARK(tl(cons(z0, hd(hd(nats))))) -> c17(A__TL(cons(z0, hd(hd(nats))))) MARK(tl(cons(z0, hd(hd(adx(y1)))))) -> c17(A__TL(cons(z0, hd(hd(adx(y1)))))) MARK(tl(cons(z0, hd(hd(incr(y1)))))) -> c17(A__TL(cons(z0, hd(hd(incr(y1)))))) MARK(tl(cons(z0, hd(hd(hd(y1)))))) -> c17(A__TL(cons(z0, hd(hd(hd(y1)))))) MARK(tl(cons(z0, hd(hd(tl(y1)))))) -> c17(A__TL(cons(z0, hd(hd(tl(y1)))))) MARK(tl(cons(z0, hd(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(hd(cons(y1, y2)))))) MARK(tl(cons(z0, hd(hd(y1))))) -> c17(A__TL(cons(z0, hd(hd(y1))))) MARK(tl(cons(z0, hd(tl(nats))))) -> c17(A__TL(cons(z0, hd(tl(nats))))) MARK(tl(cons(z0, hd(tl(adx(y1)))))) -> c17(A__TL(cons(z0, hd(tl(adx(y1)))))) MARK(tl(cons(z0, hd(tl(zeros))))) -> c17(A__TL(cons(z0, hd(tl(zeros))))) MARK(tl(cons(z0, hd(tl(incr(y1)))))) -> c17(A__TL(cons(z0, hd(tl(incr(y1)))))) MARK(tl(cons(z0, hd(tl(hd(y1)))))) -> c17(A__TL(cons(z0, hd(tl(hd(y1)))))) MARK(tl(cons(z0, hd(tl(tl(y1)))))) -> c17(A__TL(cons(z0, hd(tl(tl(y1)))))) MARK(tl(cons(z0, hd(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(tl(cons(y1, y2)))))) MARK(tl(cons(z0, hd(tl(y1))))) -> c17(A__TL(cons(z0, hd(tl(y1))))) MARK(tl(cons(z0, hd(nats)))) -> c17(A__TL(cons(z0, hd(nats)))) MARK(tl(cons(z0, tl(adx(nats))))) -> c17(A__TL(cons(z0, tl(adx(nats))))) MARK(tl(cons(z0, tl(adx(adx(y1)))))) -> c17(A__TL(cons(z0, tl(adx(adx(y1)))))) MARK(tl(cons(z0, tl(adx(zeros))))) -> c17(A__TL(cons(z0, tl(adx(zeros))))) MARK(tl(cons(z0, tl(adx(incr(y1)))))) -> c17(A__TL(cons(z0, tl(adx(incr(y1)))))) MARK(tl(cons(z0, tl(adx(hd(y1)))))) -> c17(A__TL(cons(z0, tl(adx(hd(y1)))))) MARK(tl(cons(z0, tl(adx(tl(y1)))))) -> c17(A__TL(cons(z0, tl(adx(tl(y1)))))) MARK(tl(cons(z0, tl(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(adx(cons(y1, y2)))))) MARK(tl(cons(z0, tl(adx(s(y1)))))) -> c17(A__TL(cons(z0, tl(adx(s(y1)))))) MARK(tl(cons(z0, tl(adx(y1))))) -> c17(A__TL(cons(z0, tl(adx(y1))))) MARK(tl(cons(z0, tl(incr(nats))))) -> c17(A__TL(cons(z0, tl(incr(nats))))) MARK(tl(cons(z0, tl(incr(adx(y1)))))) -> c17(A__TL(cons(z0, tl(incr(adx(y1)))))) MARK(tl(cons(z0, tl(incr(zeros))))) -> c17(A__TL(cons(z0, tl(incr(zeros))))) MARK(tl(cons(z0, tl(incr(incr(y1)))))) -> c17(A__TL(cons(z0, tl(incr(incr(y1)))))) MARK(tl(cons(z0, tl(incr(hd(y1)))))) -> c17(A__TL(cons(z0, tl(incr(hd(y1)))))) MARK(tl(cons(z0, tl(incr(tl(y1)))))) -> c17(A__TL(cons(z0, tl(incr(tl(y1)))))) MARK(tl(cons(z0, tl(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(incr(cons(y1, y2)))))) MARK(tl(cons(z0, tl(incr(0))))) -> c17(A__TL(cons(z0, tl(incr(0))))) MARK(tl(cons(z0, tl(incr(s(y1)))))) -> c17(A__TL(cons(z0, tl(incr(s(y1)))))) MARK(tl(cons(z0, tl(incr(y1))))) -> c17(A__TL(cons(z0, tl(incr(y1))))) MARK(tl(cons(z0, tl(hd(nats))))) -> c17(A__TL(cons(z0, tl(hd(nats))))) MARK(tl(cons(z0, tl(hd(adx(y1)))))) -> c17(A__TL(cons(z0, tl(hd(adx(y1)))))) MARK(tl(cons(z0, tl(hd(incr(y1)))))) -> c17(A__TL(cons(z0, tl(hd(incr(y1)))))) MARK(tl(cons(z0, tl(hd(hd(y1)))))) -> c17(A__TL(cons(z0, tl(hd(hd(y1)))))) MARK(tl(cons(z0, tl(hd(tl(y1)))))) -> c17(A__TL(cons(z0, tl(hd(tl(y1)))))) MARK(tl(cons(z0, tl(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(hd(cons(y1, y2)))))) MARK(tl(cons(z0, tl(hd(y1))))) -> c17(A__TL(cons(z0, tl(hd(y1))))) MARK(tl(cons(z0, tl(tl(nats))))) -> c17(A__TL(cons(z0, tl(tl(nats))))) MARK(tl(cons(z0, tl(tl(adx(y1)))))) -> c17(A__TL(cons(z0, tl(tl(adx(y1)))))) MARK(tl(cons(z0, tl(tl(zeros))))) -> c17(A__TL(cons(z0, tl(tl(zeros))))) MARK(tl(cons(z0, tl(tl(incr(y1)))))) -> c17(A__TL(cons(z0, tl(tl(incr(y1)))))) MARK(tl(cons(z0, tl(tl(hd(y1)))))) -> c17(A__TL(cons(z0, tl(tl(hd(y1)))))) MARK(tl(cons(z0, tl(tl(tl(y1)))))) -> c17(A__TL(cons(z0, tl(tl(tl(y1)))))) MARK(tl(cons(z0, tl(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(tl(cons(y1, y2)))))) MARK(tl(cons(z0, tl(tl(y1))))) -> c17(A__TL(cons(z0, tl(tl(y1))))) MARK(tl(cons(z0, tl(nats)))) -> c17(A__TL(cons(z0, tl(nats)))) MARK(tl(cons(z0, hd(adx(0))))) -> c17(A__TL(cons(z0, hd(adx(0))))) MARK(tl(cons(z0, hd(adx(s(y1)))))) -> c17(A__TL(cons(z0, hd(adx(s(y1)))))) MARK(tl(cons(z0, hd(incr(0))))) -> c17(A__TL(cons(z0, hd(incr(0))))) MARK(tl(cons(z0, hd(incr(s(y1)))))) -> c17(A__TL(cons(z0, hd(incr(s(y1)))))) MARK(tl(cons(z0, hd(hd(zeros))))) -> c17(A__TL(cons(z0, hd(hd(zeros))))) MARK(tl(cons(z0, tl(hd(zeros))))) -> c17(A__TL(cons(z0, tl(hd(zeros))))) MARK(tl(cons(z0, tl(adx(0))))) -> c17(A__TL(cons(z0, tl(adx(0))))) MARK(hd(adx(adx(y0)))) -> c16(MARK(adx(adx(y0)))) MARK(hd(adx(incr(y0)))) -> c16(MARK(adx(incr(y0)))) MARK(hd(adx(hd(cons(y0, y1))))) -> c16(MARK(adx(hd(cons(y0, y1))))) MARK(hd(adx(tl(cons(y0, y1))))) -> c16(MARK(adx(tl(cons(y0, y1))))) MARK(hd(adx(hd(adx(nats))))) -> c16(MARK(adx(hd(adx(nats))))) MARK(hd(adx(hd(adx(adx(y0)))))) -> c16(MARK(adx(hd(adx(adx(y0)))))) MARK(hd(adx(hd(adx(zeros))))) -> c16(MARK(adx(hd(adx(zeros))))) MARK(hd(adx(hd(adx(incr(y0)))))) -> c16(MARK(adx(hd(adx(incr(y0)))))) MARK(hd(adx(hd(adx(hd(y0)))))) -> c16(MARK(adx(hd(adx(hd(y0)))))) MARK(hd(adx(hd(adx(tl(y0)))))) -> c16(MARK(adx(hd(adx(tl(y0)))))) MARK(hd(adx(hd(adx(cons(y0, y1)))))) -> c16(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(hd(adx(hd(adx(y0))))) -> c16(MARK(adx(hd(adx(y0))))) MARK(hd(adx(hd(incr(nats))))) -> c16(MARK(adx(hd(incr(nats))))) MARK(hd(adx(hd(incr(adx(y0)))))) -> c16(MARK(adx(hd(incr(adx(y0)))))) MARK(hd(adx(hd(incr(zeros))))) -> c16(MARK(adx(hd(incr(zeros))))) MARK(hd(adx(hd(incr(incr(y0)))))) -> c16(MARK(adx(hd(incr(incr(y0)))))) MARK(hd(adx(hd(incr(hd(y0)))))) -> c16(MARK(adx(hd(incr(hd(y0)))))) MARK(hd(adx(hd(incr(tl(y0)))))) -> c16(MARK(adx(hd(incr(tl(y0)))))) MARK(hd(adx(hd(incr(cons(y0, y1)))))) -> c16(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(hd(adx(hd(incr(y0))))) -> c16(MARK(adx(hd(incr(y0))))) MARK(hd(adx(hd(hd(nats))))) -> c16(MARK(adx(hd(hd(nats))))) MARK(hd(adx(hd(hd(adx(y0)))))) -> c16(MARK(adx(hd(hd(adx(y0)))))) MARK(hd(adx(hd(hd(incr(y0)))))) -> c16(MARK(adx(hd(hd(incr(y0)))))) MARK(hd(adx(hd(hd(hd(y0)))))) -> c16(MARK(adx(hd(hd(hd(y0)))))) MARK(hd(adx(hd(hd(tl(y0)))))) -> c16(MARK(adx(hd(hd(tl(y0)))))) MARK(hd(adx(hd(hd(cons(y0, y1)))))) -> c16(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(hd(adx(hd(hd(y0))))) -> c16(MARK(adx(hd(hd(y0))))) MARK(hd(adx(hd(tl(nats))))) -> c16(MARK(adx(hd(tl(nats))))) MARK(hd(adx(hd(tl(adx(y0)))))) -> c16(MARK(adx(hd(tl(adx(y0)))))) MARK(hd(adx(hd(tl(incr(y0)))))) -> c16(MARK(adx(hd(tl(incr(y0)))))) MARK(hd(adx(hd(tl(hd(y0)))))) -> c16(MARK(adx(hd(tl(hd(y0)))))) MARK(hd(adx(hd(tl(tl(y0)))))) -> c16(MARK(adx(hd(tl(tl(y0)))))) MARK(hd(adx(hd(tl(cons(y0, y1)))))) -> c16(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(hd(adx(hd(tl(y0))))) -> c16(MARK(adx(hd(tl(y0))))) MARK(hd(adx(hd(nats)))) -> c16(MARK(adx(hd(nats)))) MARK(hd(adx(tl(adx(nats))))) -> c16(MARK(adx(tl(adx(nats))))) MARK(hd(adx(tl(adx(adx(y0)))))) -> c16(MARK(adx(tl(adx(adx(y0)))))) MARK(hd(adx(tl(adx(zeros))))) -> c16(MARK(adx(tl(adx(zeros))))) MARK(hd(adx(tl(adx(incr(y0)))))) -> c16(MARK(adx(tl(adx(incr(y0)))))) MARK(hd(adx(tl(adx(hd(y0)))))) -> c16(MARK(adx(tl(adx(hd(y0)))))) MARK(hd(adx(tl(adx(tl(y0)))))) -> c16(MARK(adx(tl(adx(tl(y0)))))) MARK(hd(adx(tl(adx(cons(y0, y1)))))) -> c16(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(hd(adx(tl(adx(y0))))) -> c16(MARK(adx(tl(adx(y0))))) MARK(hd(adx(tl(incr(nats))))) -> c16(MARK(adx(tl(incr(nats))))) MARK(hd(adx(tl(incr(adx(y0)))))) -> c16(MARK(adx(tl(incr(adx(y0)))))) MARK(hd(adx(tl(incr(zeros))))) -> c16(MARK(adx(tl(incr(zeros))))) MARK(hd(adx(tl(incr(incr(y0)))))) -> c16(MARK(adx(tl(incr(incr(y0)))))) MARK(hd(adx(tl(incr(hd(y0)))))) -> c16(MARK(adx(tl(incr(hd(y0)))))) MARK(hd(adx(tl(incr(tl(y0)))))) -> c16(MARK(adx(tl(incr(tl(y0)))))) MARK(hd(adx(tl(incr(cons(y0, y1)))))) -> c16(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(hd(adx(tl(incr(s(y0)))))) -> c16(MARK(adx(tl(incr(s(y0)))))) MARK(hd(adx(tl(incr(y0))))) -> c16(MARK(adx(tl(incr(y0))))) MARK(hd(adx(tl(hd(nats))))) -> c16(MARK(adx(tl(hd(nats))))) MARK(hd(adx(tl(hd(adx(y0)))))) -> c16(MARK(adx(tl(hd(adx(y0)))))) MARK(hd(adx(tl(hd(incr(y0)))))) -> c16(MARK(adx(tl(hd(incr(y0)))))) MARK(hd(adx(tl(hd(hd(y0)))))) -> c16(MARK(adx(tl(hd(hd(y0)))))) MARK(hd(adx(tl(hd(tl(y0)))))) -> c16(MARK(adx(tl(hd(tl(y0)))))) MARK(hd(adx(tl(hd(cons(y0, y1)))))) -> c16(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(hd(adx(tl(hd(y0))))) -> c16(MARK(adx(tl(hd(y0))))) MARK(hd(adx(tl(tl(nats))))) -> c16(MARK(adx(tl(tl(nats))))) MARK(hd(adx(tl(tl(adx(y0)))))) -> c16(MARK(adx(tl(tl(adx(y0)))))) MARK(hd(adx(tl(tl(incr(y0)))))) -> c16(MARK(adx(tl(tl(incr(y0)))))) MARK(hd(adx(tl(tl(hd(y0)))))) -> c16(MARK(adx(tl(tl(hd(y0)))))) MARK(hd(adx(tl(tl(tl(y0)))))) -> c16(MARK(adx(tl(tl(tl(y0)))))) MARK(hd(adx(tl(tl(cons(y0, y1)))))) -> c16(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(hd(adx(tl(tl(y0))))) -> c16(MARK(adx(tl(tl(y0))))) MARK(hd(adx(tl(nats)))) -> c16(MARK(adx(tl(nats)))) MARK(hd(adx(hd(adx(0))))) -> c16(MARK(adx(hd(adx(0))))) MARK(hd(adx(hd(adx(s(y0)))))) -> c16(MARK(adx(hd(adx(s(y0)))))) MARK(hd(adx(hd(incr(0))))) -> c16(MARK(adx(hd(incr(0))))) MARK(hd(adx(hd(incr(s(y0)))))) -> c16(MARK(adx(hd(incr(s(y0)))))) MARK(hd(adx(hd(hd(zeros))))) -> c16(MARK(adx(hd(hd(zeros))))) MARK(hd(adx(tl(hd(zeros))))) -> c16(MARK(adx(tl(hd(zeros))))) MARK(hd(adx(tl(adx(0))))) -> c16(MARK(adx(tl(adx(0))))) MARK(hd(adx(hd(tl(zeros))))) -> c16(MARK(adx(hd(tl(zeros))))) MARK(hd(adx(tl(tl(zeros))))) -> c16(MARK(adx(tl(tl(zeros))))) MARK(hd(adx(tl(adx(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) MARK(hd(adx(tl(incr(0))))) -> c16(MARK(adx(tl(incr(0))))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c16_2, c16_1, c17_2, c17_1, c8_1, c10_1, c13_1, c15_1 ---------------------------------------- (207) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) by MARK(hd(incr(incr(y0)))) -> c16(MARK(incr(incr(y0)))) MARK(hd(incr(hd(cons(y0, y1))))) -> c16(MARK(incr(hd(cons(y0, y1))))) MARK(hd(incr(tl(cons(y0, y1))))) -> c16(MARK(incr(tl(cons(y0, y1))))) MARK(hd(incr(hd(adx(adx(y0)))))) -> c16(MARK(incr(hd(adx(adx(y0)))))) MARK(hd(incr(hd(adx(incr(y0)))))) -> c16(MARK(incr(hd(adx(incr(y0)))))) MARK(hd(incr(hd(adx(hd(y0)))))) -> c16(MARK(incr(hd(adx(hd(y0)))))) MARK(hd(incr(hd(adx(tl(y0)))))) -> c16(MARK(incr(hd(adx(tl(y0)))))) MARK(hd(incr(hd(adx(y0))))) -> c16(MARK(incr(hd(adx(y0))))) MARK(hd(incr(hd(incr(nats))))) -> c16(MARK(incr(hd(incr(nats))))) MARK(hd(incr(hd(incr(adx(y0)))))) -> c16(MARK(incr(hd(incr(adx(y0)))))) MARK(hd(incr(hd(incr(zeros))))) -> c16(MARK(incr(hd(incr(zeros))))) MARK(hd(incr(hd(incr(incr(y0)))))) -> c16(MARK(incr(hd(incr(incr(y0)))))) MARK(hd(incr(hd(incr(hd(y0)))))) -> c16(MARK(incr(hd(incr(hd(y0)))))) MARK(hd(incr(hd(incr(tl(y0)))))) -> c16(MARK(incr(hd(incr(tl(y0)))))) MARK(hd(incr(hd(incr(cons(y0, y1)))))) -> c16(MARK(incr(hd(incr(cons(y0, y1)))))) MARK(hd(incr(hd(incr(y0))))) -> c16(MARK(incr(hd(incr(y0))))) MARK(hd(incr(hd(hd(nats))))) -> c16(MARK(incr(hd(hd(nats))))) MARK(hd(incr(hd(hd(adx(y0)))))) -> c16(MARK(incr(hd(hd(adx(y0)))))) MARK(hd(incr(hd(hd(incr(y0)))))) -> c16(MARK(incr(hd(hd(incr(y0)))))) MARK(hd(incr(hd(hd(hd(y0)))))) -> c16(MARK(incr(hd(hd(hd(y0)))))) MARK(hd(incr(hd(hd(tl(y0)))))) -> c16(MARK(incr(hd(hd(tl(y0)))))) MARK(hd(incr(hd(hd(cons(y0, y1)))))) -> c16(MARK(incr(hd(hd(cons(y0, y1)))))) MARK(hd(incr(hd(hd(y0))))) -> c16(MARK(incr(hd(hd(y0))))) MARK(hd(incr(hd(tl(nats))))) -> c16(MARK(incr(hd(tl(nats))))) MARK(hd(incr(hd(tl(adx(y0)))))) -> c16(MARK(incr(hd(tl(adx(y0)))))) MARK(hd(incr(hd(tl(incr(y0)))))) -> c16(MARK(incr(hd(tl(incr(y0)))))) MARK(hd(incr(hd(tl(hd(y0)))))) -> c16(MARK(incr(hd(tl(hd(y0)))))) MARK(hd(incr(hd(tl(tl(y0)))))) -> c16(MARK(incr(hd(tl(tl(y0)))))) MARK(hd(incr(hd(tl(cons(y0, y1)))))) -> c16(MARK(incr(hd(tl(cons(y0, y1)))))) MARK(hd(incr(hd(tl(y0))))) -> c16(MARK(incr(hd(tl(y0))))) MARK(hd(incr(hd(nats)))) -> c16(MARK(incr(hd(nats)))) MARK(hd(incr(tl(adx(adx(y0)))))) -> c16(MARK(incr(tl(adx(adx(y0)))))) MARK(hd(incr(tl(adx(incr(y0)))))) -> c16(MARK(incr(tl(adx(incr(y0)))))) MARK(hd(incr(tl(adx(hd(y0)))))) -> c16(MARK(incr(tl(adx(hd(y0)))))) MARK(hd(incr(tl(adx(tl(y0)))))) -> c16(MARK(incr(tl(adx(tl(y0)))))) MARK(hd(incr(tl(adx(y0))))) -> c16(MARK(incr(tl(adx(y0))))) MARK(hd(incr(tl(incr(nats))))) -> c16(MARK(incr(tl(incr(nats))))) MARK(hd(incr(tl(incr(adx(y0)))))) -> c16(MARK(incr(tl(incr(adx(y0)))))) MARK(hd(incr(tl(incr(zeros))))) -> c16(MARK(incr(tl(incr(zeros))))) MARK(hd(incr(tl(incr(incr(y0)))))) -> c16(MARK(incr(tl(incr(incr(y0)))))) MARK(hd(incr(tl(incr(hd(y0)))))) -> c16(MARK(incr(tl(incr(hd(y0)))))) MARK(hd(incr(tl(incr(tl(y0)))))) -> c16(MARK(incr(tl(incr(tl(y0)))))) MARK(hd(incr(tl(incr(cons(y0, y1)))))) -> c16(MARK(incr(tl(incr(cons(y0, y1)))))) MARK(hd(incr(tl(incr(y0))))) -> c16(MARK(incr(tl(incr(y0))))) MARK(hd(incr(tl(hd(nats))))) -> c16(MARK(incr(tl(hd(nats))))) MARK(hd(incr(tl(hd(adx(y0)))))) -> c16(MARK(incr(tl(hd(adx(y0)))))) MARK(hd(incr(tl(hd(incr(y0)))))) -> c16(MARK(incr(tl(hd(incr(y0)))))) MARK(hd(incr(tl(hd(hd(y0)))))) -> c16(MARK(incr(tl(hd(hd(y0)))))) MARK(hd(incr(tl(hd(tl(y0)))))) -> c16(MARK(incr(tl(hd(tl(y0)))))) MARK(hd(incr(tl(hd(cons(y0, y1)))))) -> c16(MARK(incr(tl(hd(cons(y0, y1)))))) MARK(hd(incr(tl(hd(y0))))) -> c16(MARK(incr(tl(hd(y0))))) MARK(hd(incr(tl(tl(nats))))) -> c16(MARK(incr(tl(tl(nats))))) MARK(hd(incr(tl(tl(adx(y0)))))) -> c16(MARK(incr(tl(tl(adx(y0)))))) MARK(hd(incr(tl(tl(incr(y0)))))) -> c16(MARK(incr(tl(tl(incr(y0)))))) MARK(hd(incr(tl(tl(hd(y0)))))) -> c16(MARK(incr(tl(tl(hd(y0)))))) MARK(hd(incr(tl(tl(tl(y0)))))) -> c16(MARK(incr(tl(tl(tl(y0)))))) MARK(hd(incr(tl(tl(cons(y0, y1)))))) -> c16(MARK(incr(tl(tl(cons(y0, y1)))))) MARK(hd(incr(tl(tl(y0))))) -> c16(MARK(incr(tl(tl(y0))))) MARK(hd(incr(tl(nats)))) -> c16(MARK(incr(tl(nats)))) MARK(hd(incr(hd(incr(0))))) -> c16(MARK(incr(hd(incr(0))))) MARK(hd(incr(hd(incr(s(y0)))))) -> c16(MARK(incr(hd(incr(s(y0)))))) MARK(hd(incr(hd(hd(zeros))))) -> c16(MARK(incr(hd(hd(zeros))))) MARK(hd(incr(tl(hd(zeros))))) -> c16(MARK(incr(tl(hd(zeros))))) MARK(hd(incr(hd(tl(zeros))))) -> c16(MARK(incr(hd(tl(zeros))))) MARK(hd(incr(tl(tl(zeros))))) -> c16(MARK(incr(tl(tl(zeros))))) MARK(hd(incr(tl(incr(0))))) -> c16(MARK(incr(tl(incr(0))))) MARK(hd(incr(adx(adx(y0))))) -> c16(MARK(incr(adx(adx(y0))))) MARK(hd(incr(adx(incr(y0))))) -> c16(MARK(incr(adx(incr(y0))))) MARK(hd(incr(adx(hd(cons(y0, y1)))))) -> c16(MARK(incr(adx(hd(cons(y0, y1)))))) MARK(hd(incr(adx(tl(cons(y0, y1)))))) -> c16(MARK(incr(adx(tl(cons(y0, y1)))))) MARK(hd(incr(adx(hd(adx(nats)))))) -> c16(MARK(incr(adx(hd(adx(nats)))))) MARK(hd(incr(adx(hd(adx(adx(y0))))))) -> c16(MARK(incr(adx(hd(adx(adx(y0))))))) MARK(hd(incr(adx(hd(adx(zeros)))))) -> c16(MARK(incr(adx(hd(adx(zeros)))))) MARK(hd(incr(adx(hd(adx(incr(y0))))))) -> c16(MARK(incr(adx(hd(adx(incr(y0))))))) MARK(hd(incr(adx(hd(adx(hd(y0))))))) -> c16(MARK(incr(adx(hd(adx(hd(y0))))))) MARK(hd(incr(adx(hd(adx(tl(y0))))))) -> c16(MARK(incr(adx(hd(adx(tl(y0))))))) MARK(hd(incr(adx(hd(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(adx(cons(y0, y1))))))) MARK(hd(incr(adx(hd(adx(y0)))))) -> c16(MARK(incr(adx(hd(adx(y0)))))) MARK(hd(incr(adx(hd(incr(nats)))))) -> c16(MARK(incr(adx(hd(incr(nats)))))) MARK(hd(incr(adx(hd(incr(adx(y0))))))) -> c16(MARK(incr(adx(hd(incr(adx(y0))))))) MARK(hd(incr(adx(hd(incr(zeros)))))) -> c16(MARK(incr(adx(hd(incr(zeros)))))) MARK(hd(incr(adx(hd(incr(incr(y0))))))) -> c16(MARK(incr(adx(hd(incr(incr(y0))))))) MARK(hd(incr(adx(hd(incr(hd(y0))))))) -> c16(MARK(incr(adx(hd(incr(hd(y0))))))) MARK(hd(incr(adx(hd(incr(tl(y0))))))) -> c16(MARK(incr(adx(hd(incr(tl(y0))))))) MARK(hd(incr(adx(hd(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(incr(cons(y0, y1))))))) MARK(hd(incr(adx(hd(incr(y0)))))) -> c16(MARK(incr(adx(hd(incr(y0)))))) MARK(hd(incr(adx(hd(hd(nats)))))) -> c16(MARK(incr(adx(hd(hd(nats)))))) MARK(hd(incr(adx(hd(hd(adx(y0))))))) -> c16(MARK(incr(adx(hd(hd(adx(y0))))))) MARK(hd(incr(adx(hd(hd(incr(y0))))))) -> c16(MARK(incr(adx(hd(hd(incr(y0))))))) MARK(hd(incr(adx(hd(hd(hd(y0))))))) -> c16(MARK(incr(adx(hd(hd(hd(y0))))))) MARK(hd(incr(adx(hd(hd(tl(y0))))))) -> c16(MARK(incr(adx(hd(hd(tl(y0))))))) MARK(hd(incr(adx(hd(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(hd(cons(y0, y1))))))) MARK(hd(incr(adx(hd(hd(y0)))))) -> c16(MARK(incr(adx(hd(hd(y0)))))) MARK(hd(incr(adx(hd(tl(nats)))))) -> c16(MARK(incr(adx(hd(tl(nats)))))) MARK(hd(incr(adx(hd(tl(adx(y0))))))) -> c16(MARK(incr(adx(hd(tl(adx(y0))))))) MARK(hd(incr(adx(hd(tl(incr(y0))))))) -> c16(MARK(incr(adx(hd(tl(incr(y0))))))) MARK(hd(incr(adx(hd(tl(hd(y0))))))) -> c16(MARK(incr(adx(hd(tl(hd(y0))))))) MARK(hd(incr(adx(hd(tl(tl(y0))))))) -> c16(MARK(incr(adx(hd(tl(tl(y0))))))) MARK(hd(incr(adx(hd(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(tl(cons(y0, y1))))))) MARK(hd(incr(adx(hd(tl(y0)))))) -> c16(MARK(incr(adx(hd(tl(y0)))))) MARK(hd(incr(adx(hd(nats))))) -> c16(MARK(incr(adx(hd(nats))))) MARK(hd(incr(adx(tl(adx(nats)))))) -> c16(MARK(incr(adx(tl(adx(nats)))))) MARK(hd(incr(adx(tl(adx(adx(y0))))))) -> c16(MARK(incr(adx(tl(adx(adx(y0))))))) MARK(hd(incr(adx(tl(adx(zeros)))))) -> c16(MARK(incr(adx(tl(adx(zeros)))))) MARK(hd(incr(adx(tl(adx(incr(y0))))))) -> c16(MARK(incr(adx(tl(adx(incr(y0))))))) MARK(hd(incr(adx(tl(adx(hd(y0))))))) -> c16(MARK(incr(adx(tl(adx(hd(y0))))))) MARK(hd(incr(adx(tl(adx(tl(y0))))))) -> c16(MARK(incr(adx(tl(adx(tl(y0))))))) MARK(hd(incr(adx(tl(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(adx(cons(y0, y1))))))) MARK(hd(incr(adx(tl(adx(y0)))))) -> c16(MARK(incr(adx(tl(adx(y0)))))) MARK(hd(incr(adx(tl(incr(nats)))))) -> c16(MARK(incr(adx(tl(incr(nats)))))) MARK(hd(incr(adx(tl(incr(adx(y0))))))) -> c16(MARK(incr(adx(tl(incr(adx(y0))))))) MARK(hd(incr(adx(tl(incr(zeros)))))) -> c16(MARK(incr(adx(tl(incr(zeros)))))) MARK(hd(incr(adx(tl(incr(incr(y0))))))) -> c16(MARK(incr(adx(tl(incr(incr(y0))))))) MARK(hd(incr(adx(tl(incr(hd(y0))))))) -> c16(MARK(incr(adx(tl(incr(hd(y0))))))) MARK(hd(incr(adx(tl(incr(tl(y0))))))) -> c16(MARK(incr(adx(tl(incr(tl(y0))))))) MARK(hd(incr(adx(tl(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(incr(cons(y0, y1))))))) MARK(hd(incr(adx(tl(incr(s(y0))))))) -> c16(MARK(incr(adx(tl(incr(s(y0))))))) MARK(hd(incr(adx(tl(incr(y0)))))) -> c16(MARK(incr(adx(tl(incr(y0)))))) MARK(hd(incr(adx(tl(hd(nats)))))) -> c16(MARK(incr(adx(tl(hd(nats)))))) MARK(hd(incr(adx(tl(hd(adx(y0))))))) -> c16(MARK(incr(adx(tl(hd(adx(y0))))))) MARK(hd(incr(adx(tl(hd(incr(y0))))))) -> c16(MARK(incr(adx(tl(hd(incr(y0))))))) MARK(hd(incr(adx(tl(hd(hd(y0))))))) -> c16(MARK(incr(adx(tl(hd(hd(y0))))))) MARK(hd(incr(adx(tl(hd(tl(y0))))))) -> c16(MARK(incr(adx(tl(hd(tl(y0))))))) MARK(hd(incr(adx(tl(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(hd(cons(y0, y1))))))) MARK(hd(incr(adx(tl(hd(y0)))))) -> c16(MARK(incr(adx(tl(hd(y0)))))) MARK(hd(incr(adx(tl(tl(nats)))))) -> c16(MARK(incr(adx(tl(tl(nats)))))) MARK(hd(incr(adx(tl(tl(adx(y0))))))) -> c16(MARK(incr(adx(tl(tl(adx(y0))))))) MARK(hd(incr(adx(tl(tl(incr(y0))))))) -> c16(MARK(incr(adx(tl(tl(incr(y0))))))) MARK(hd(incr(adx(tl(tl(hd(y0))))))) -> c16(MARK(incr(adx(tl(tl(hd(y0))))))) MARK(hd(incr(adx(tl(tl(tl(y0))))))) -> c16(MARK(incr(adx(tl(tl(tl(y0))))))) MARK(hd(incr(adx(tl(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(tl(cons(y0, y1))))))) MARK(hd(incr(adx(tl(tl(y0)))))) -> c16(MARK(incr(adx(tl(tl(y0)))))) MARK(hd(incr(adx(tl(nats))))) -> c16(MARK(incr(adx(tl(nats))))) MARK(hd(incr(adx(hd(adx(0)))))) -> c16(MARK(incr(adx(hd(adx(0)))))) MARK(hd(incr(adx(hd(adx(s(y0))))))) -> c16(MARK(incr(adx(hd(adx(s(y0))))))) MARK(hd(incr(adx(hd(incr(0)))))) -> c16(MARK(incr(adx(hd(incr(0)))))) MARK(hd(incr(adx(hd(incr(s(y0))))))) -> c16(MARK(incr(adx(hd(incr(s(y0))))))) MARK(hd(incr(adx(hd(hd(zeros)))))) -> c16(MARK(incr(adx(hd(hd(zeros)))))) MARK(hd(incr(adx(tl(hd(zeros)))))) -> c16(MARK(incr(adx(tl(hd(zeros)))))) MARK(hd(incr(adx(tl(adx(0)))))) -> c16(MARK(incr(adx(tl(adx(0)))))) MARK(hd(incr(adx(hd(tl(zeros)))))) -> c16(MARK(incr(adx(hd(tl(zeros)))))) MARK(hd(incr(adx(tl(tl(zeros)))))) -> c16(MARK(incr(adx(tl(tl(zeros)))))) MARK(hd(incr(adx(tl(adx(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) MARK(hd(incr(adx(tl(incr(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) MARK(hd(incr(hd(adx(nats))))) -> c16(MARK(incr(hd(adx(nats))))) MARK(hd(incr(hd(adx(zeros))))) -> c16(MARK(incr(hd(adx(zeros))))) MARK(hd(incr(hd(adx(cons(y0, y1)))))) -> c16(MARK(incr(hd(adx(cons(y0, y1)))))) MARK(hd(incr(tl(adx(nats))))) -> c16(MARK(incr(tl(adx(nats))))) MARK(hd(incr(tl(adx(zeros))))) -> c16(MARK(incr(tl(adx(zeros))))) MARK(hd(incr(tl(adx(cons(y0, y1)))))) -> c16(MARK(incr(tl(adx(cons(y0, y1)))))) MARK(hd(incr(tl(incr(s(y0)))))) -> c16(MARK(incr(tl(incr(s(y0)))))) ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) MARK(tl(cons(z0, adx(y1)))) -> c17(A__TL(cons(z0, adx(y1)))) MARK(tl(cons(z0, incr(y1)))) -> c17(A__TL(cons(z0, incr(y1)))) MARK(tl(cons(z0, hd(cons(y1, y2))))) -> c17(A__TL(cons(z0, hd(cons(y1, y2))))) MARK(tl(cons(z0, tl(cons(y1, y2))))) -> c17(A__TL(cons(z0, tl(cons(y1, y2))))) MARK(tl(cons(z0, hd(adx(nats))))) -> c17(A__TL(cons(z0, hd(adx(nats))))) MARK(tl(cons(z0, hd(adx(adx(y1)))))) -> c17(A__TL(cons(z0, hd(adx(adx(y1)))))) MARK(tl(cons(z0, hd(adx(zeros))))) -> c17(A__TL(cons(z0, hd(adx(zeros))))) MARK(tl(cons(z0, hd(adx(incr(y1)))))) -> c17(A__TL(cons(z0, hd(adx(incr(y1)))))) MARK(tl(cons(z0, hd(adx(hd(y1)))))) -> c17(A__TL(cons(z0, hd(adx(hd(y1)))))) MARK(tl(cons(z0, hd(adx(tl(y1)))))) -> c17(A__TL(cons(z0, hd(adx(tl(y1)))))) MARK(tl(cons(z0, hd(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(adx(cons(y1, y2)))))) MARK(tl(cons(z0, hd(adx(y1))))) -> c17(A__TL(cons(z0, hd(adx(y1))))) MARK(tl(cons(z0, hd(incr(nats))))) -> c17(A__TL(cons(z0, hd(incr(nats))))) MARK(tl(cons(z0, hd(incr(adx(y1)))))) -> c17(A__TL(cons(z0, hd(incr(adx(y1)))))) MARK(tl(cons(z0, hd(incr(zeros))))) -> c17(A__TL(cons(z0, hd(incr(zeros))))) MARK(tl(cons(z0, hd(incr(incr(y1)))))) -> c17(A__TL(cons(z0, hd(incr(incr(y1)))))) MARK(tl(cons(z0, hd(incr(hd(y1)))))) -> c17(A__TL(cons(z0, hd(incr(hd(y1)))))) MARK(tl(cons(z0, hd(incr(tl(y1)))))) -> c17(A__TL(cons(z0, hd(incr(tl(y1)))))) MARK(tl(cons(z0, hd(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(incr(cons(y1, y2)))))) MARK(tl(cons(z0, hd(incr(y1))))) -> c17(A__TL(cons(z0, hd(incr(y1))))) MARK(tl(cons(z0, hd(hd(nats))))) -> c17(A__TL(cons(z0, hd(hd(nats))))) MARK(tl(cons(z0, hd(hd(adx(y1)))))) -> c17(A__TL(cons(z0, hd(hd(adx(y1)))))) MARK(tl(cons(z0, hd(hd(incr(y1)))))) -> c17(A__TL(cons(z0, hd(hd(incr(y1)))))) MARK(tl(cons(z0, hd(hd(hd(y1)))))) -> c17(A__TL(cons(z0, hd(hd(hd(y1)))))) MARK(tl(cons(z0, hd(hd(tl(y1)))))) -> c17(A__TL(cons(z0, hd(hd(tl(y1)))))) MARK(tl(cons(z0, hd(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(hd(cons(y1, y2)))))) MARK(tl(cons(z0, hd(hd(y1))))) -> c17(A__TL(cons(z0, hd(hd(y1))))) MARK(tl(cons(z0, hd(tl(nats))))) -> c17(A__TL(cons(z0, hd(tl(nats))))) MARK(tl(cons(z0, hd(tl(adx(y1)))))) -> c17(A__TL(cons(z0, hd(tl(adx(y1)))))) MARK(tl(cons(z0, hd(tl(zeros))))) -> c17(A__TL(cons(z0, hd(tl(zeros))))) MARK(tl(cons(z0, hd(tl(incr(y1)))))) -> c17(A__TL(cons(z0, hd(tl(incr(y1)))))) MARK(tl(cons(z0, hd(tl(hd(y1)))))) -> c17(A__TL(cons(z0, hd(tl(hd(y1)))))) MARK(tl(cons(z0, hd(tl(tl(y1)))))) -> c17(A__TL(cons(z0, hd(tl(tl(y1)))))) MARK(tl(cons(z0, hd(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(tl(cons(y1, y2)))))) MARK(tl(cons(z0, hd(tl(y1))))) -> c17(A__TL(cons(z0, hd(tl(y1))))) MARK(tl(cons(z0, hd(nats)))) -> c17(A__TL(cons(z0, hd(nats)))) MARK(tl(cons(z0, tl(adx(nats))))) -> c17(A__TL(cons(z0, tl(adx(nats))))) MARK(tl(cons(z0, tl(adx(adx(y1)))))) -> c17(A__TL(cons(z0, tl(adx(adx(y1)))))) MARK(tl(cons(z0, tl(adx(zeros))))) -> c17(A__TL(cons(z0, tl(adx(zeros))))) MARK(tl(cons(z0, tl(adx(incr(y1)))))) -> c17(A__TL(cons(z0, tl(adx(incr(y1)))))) MARK(tl(cons(z0, tl(adx(hd(y1)))))) -> c17(A__TL(cons(z0, tl(adx(hd(y1)))))) MARK(tl(cons(z0, tl(adx(tl(y1)))))) -> c17(A__TL(cons(z0, tl(adx(tl(y1)))))) MARK(tl(cons(z0, tl(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(adx(cons(y1, y2)))))) MARK(tl(cons(z0, tl(adx(s(y1)))))) -> c17(A__TL(cons(z0, tl(adx(s(y1)))))) MARK(tl(cons(z0, tl(adx(y1))))) -> c17(A__TL(cons(z0, tl(adx(y1))))) MARK(tl(cons(z0, tl(incr(nats))))) -> c17(A__TL(cons(z0, tl(incr(nats))))) MARK(tl(cons(z0, tl(incr(adx(y1)))))) -> c17(A__TL(cons(z0, tl(incr(adx(y1)))))) MARK(tl(cons(z0, tl(incr(zeros))))) -> c17(A__TL(cons(z0, tl(incr(zeros))))) MARK(tl(cons(z0, tl(incr(incr(y1)))))) -> c17(A__TL(cons(z0, tl(incr(incr(y1)))))) MARK(tl(cons(z0, tl(incr(hd(y1)))))) -> c17(A__TL(cons(z0, tl(incr(hd(y1)))))) MARK(tl(cons(z0, tl(incr(tl(y1)))))) -> c17(A__TL(cons(z0, tl(incr(tl(y1)))))) MARK(tl(cons(z0, tl(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(incr(cons(y1, y2)))))) MARK(tl(cons(z0, tl(incr(0))))) -> c17(A__TL(cons(z0, tl(incr(0))))) MARK(tl(cons(z0, tl(incr(s(y1)))))) -> c17(A__TL(cons(z0, tl(incr(s(y1)))))) MARK(tl(cons(z0, tl(incr(y1))))) -> c17(A__TL(cons(z0, tl(incr(y1))))) MARK(tl(cons(z0, tl(hd(nats))))) -> c17(A__TL(cons(z0, tl(hd(nats))))) MARK(tl(cons(z0, tl(hd(adx(y1)))))) -> c17(A__TL(cons(z0, tl(hd(adx(y1)))))) MARK(tl(cons(z0, tl(hd(incr(y1)))))) -> c17(A__TL(cons(z0, tl(hd(incr(y1)))))) MARK(tl(cons(z0, tl(hd(hd(y1)))))) -> c17(A__TL(cons(z0, tl(hd(hd(y1)))))) MARK(tl(cons(z0, tl(hd(tl(y1)))))) -> c17(A__TL(cons(z0, tl(hd(tl(y1)))))) MARK(tl(cons(z0, tl(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(hd(cons(y1, y2)))))) MARK(tl(cons(z0, tl(hd(y1))))) -> c17(A__TL(cons(z0, tl(hd(y1))))) MARK(tl(cons(z0, tl(tl(nats))))) -> c17(A__TL(cons(z0, tl(tl(nats))))) MARK(tl(cons(z0, tl(tl(adx(y1)))))) -> c17(A__TL(cons(z0, tl(tl(adx(y1)))))) MARK(tl(cons(z0, tl(tl(zeros))))) -> c17(A__TL(cons(z0, tl(tl(zeros))))) MARK(tl(cons(z0, tl(tl(incr(y1)))))) -> c17(A__TL(cons(z0, tl(tl(incr(y1)))))) MARK(tl(cons(z0, tl(tl(hd(y1)))))) -> c17(A__TL(cons(z0, tl(tl(hd(y1)))))) MARK(tl(cons(z0, tl(tl(tl(y1)))))) -> c17(A__TL(cons(z0, tl(tl(tl(y1)))))) MARK(tl(cons(z0, tl(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(tl(cons(y1, y2)))))) MARK(tl(cons(z0, tl(tl(y1))))) -> c17(A__TL(cons(z0, tl(tl(y1))))) MARK(tl(cons(z0, tl(nats)))) -> c17(A__TL(cons(z0, tl(nats)))) MARK(tl(cons(z0, hd(adx(0))))) -> c17(A__TL(cons(z0, hd(adx(0))))) MARK(tl(cons(z0, hd(adx(s(y1)))))) -> c17(A__TL(cons(z0, hd(adx(s(y1)))))) MARK(tl(cons(z0, hd(incr(0))))) -> c17(A__TL(cons(z0, hd(incr(0))))) MARK(tl(cons(z0, hd(incr(s(y1)))))) -> c17(A__TL(cons(z0, hd(incr(s(y1)))))) MARK(tl(cons(z0, hd(hd(zeros))))) -> c17(A__TL(cons(z0, hd(hd(zeros))))) MARK(tl(cons(z0, tl(hd(zeros))))) -> c17(A__TL(cons(z0, tl(hd(zeros))))) MARK(tl(cons(z0, tl(adx(0))))) -> c17(A__TL(cons(z0, tl(adx(0))))) MARK(hd(adx(adx(y0)))) -> c16(MARK(adx(adx(y0)))) MARK(hd(adx(incr(y0)))) -> c16(MARK(adx(incr(y0)))) MARK(hd(adx(hd(cons(y0, y1))))) -> c16(MARK(adx(hd(cons(y0, y1))))) MARK(hd(adx(tl(cons(y0, y1))))) -> c16(MARK(adx(tl(cons(y0, y1))))) MARK(hd(adx(hd(adx(nats))))) -> c16(MARK(adx(hd(adx(nats))))) MARK(hd(adx(hd(adx(adx(y0)))))) -> c16(MARK(adx(hd(adx(adx(y0)))))) MARK(hd(adx(hd(adx(zeros))))) -> c16(MARK(adx(hd(adx(zeros))))) MARK(hd(adx(hd(adx(incr(y0)))))) -> c16(MARK(adx(hd(adx(incr(y0)))))) MARK(hd(adx(hd(adx(hd(y0)))))) -> c16(MARK(adx(hd(adx(hd(y0)))))) MARK(hd(adx(hd(adx(tl(y0)))))) -> c16(MARK(adx(hd(adx(tl(y0)))))) MARK(hd(adx(hd(adx(cons(y0, y1)))))) -> c16(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(hd(adx(hd(adx(y0))))) -> c16(MARK(adx(hd(adx(y0))))) MARK(hd(adx(hd(incr(nats))))) -> c16(MARK(adx(hd(incr(nats))))) MARK(hd(adx(hd(incr(adx(y0)))))) -> c16(MARK(adx(hd(incr(adx(y0)))))) MARK(hd(adx(hd(incr(zeros))))) -> c16(MARK(adx(hd(incr(zeros))))) MARK(hd(adx(hd(incr(incr(y0)))))) -> c16(MARK(adx(hd(incr(incr(y0)))))) MARK(hd(adx(hd(incr(hd(y0)))))) -> c16(MARK(adx(hd(incr(hd(y0)))))) MARK(hd(adx(hd(incr(tl(y0)))))) -> c16(MARK(adx(hd(incr(tl(y0)))))) MARK(hd(adx(hd(incr(cons(y0, y1)))))) -> c16(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(hd(adx(hd(incr(y0))))) -> c16(MARK(adx(hd(incr(y0))))) MARK(hd(adx(hd(hd(nats))))) -> c16(MARK(adx(hd(hd(nats))))) MARK(hd(adx(hd(hd(adx(y0)))))) -> c16(MARK(adx(hd(hd(adx(y0)))))) MARK(hd(adx(hd(hd(incr(y0)))))) -> c16(MARK(adx(hd(hd(incr(y0)))))) MARK(hd(adx(hd(hd(hd(y0)))))) -> c16(MARK(adx(hd(hd(hd(y0)))))) MARK(hd(adx(hd(hd(tl(y0)))))) -> c16(MARK(adx(hd(hd(tl(y0)))))) MARK(hd(adx(hd(hd(cons(y0, y1)))))) -> c16(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(hd(adx(hd(hd(y0))))) -> c16(MARK(adx(hd(hd(y0))))) MARK(hd(adx(hd(tl(nats))))) -> c16(MARK(adx(hd(tl(nats))))) MARK(hd(adx(hd(tl(adx(y0)))))) -> c16(MARK(adx(hd(tl(adx(y0)))))) MARK(hd(adx(hd(tl(incr(y0)))))) -> c16(MARK(adx(hd(tl(incr(y0)))))) MARK(hd(adx(hd(tl(hd(y0)))))) -> c16(MARK(adx(hd(tl(hd(y0)))))) MARK(hd(adx(hd(tl(tl(y0)))))) -> c16(MARK(adx(hd(tl(tl(y0)))))) MARK(hd(adx(hd(tl(cons(y0, y1)))))) -> c16(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(hd(adx(hd(tl(y0))))) -> c16(MARK(adx(hd(tl(y0))))) MARK(hd(adx(hd(nats)))) -> c16(MARK(adx(hd(nats)))) MARK(hd(adx(tl(adx(nats))))) -> c16(MARK(adx(tl(adx(nats))))) MARK(hd(adx(tl(adx(adx(y0)))))) -> c16(MARK(adx(tl(adx(adx(y0)))))) MARK(hd(adx(tl(adx(zeros))))) -> c16(MARK(adx(tl(adx(zeros))))) MARK(hd(adx(tl(adx(incr(y0)))))) -> c16(MARK(adx(tl(adx(incr(y0)))))) MARK(hd(adx(tl(adx(hd(y0)))))) -> c16(MARK(adx(tl(adx(hd(y0)))))) MARK(hd(adx(tl(adx(tl(y0)))))) -> c16(MARK(adx(tl(adx(tl(y0)))))) MARK(hd(adx(tl(adx(cons(y0, y1)))))) -> c16(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(hd(adx(tl(adx(y0))))) -> c16(MARK(adx(tl(adx(y0))))) MARK(hd(adx(tl(incr(nats))))) -> c16(MARK(adx(tl(incr(nats))))) MARK(hd(adx(tl(incr(adx(y0)))))) -> c16(MARK(adx(tl(incr(adx(y0)))))) MARK(hd(adx(tl(incr(zeros))))) -> c16(MARK(adx(tl(incr(zeros))))) MARK(hd(adx(tl(incr(incr(y0)))))) -> c16(MARK(adx(tl(incr(incr(y0)))))) MARK(hd(adx(tl(incr(hd(y0)))))) -> c16(MARK(adx(tl(incr(hd(y0)))))) MARK(hd(adx(tl(incr(tl(y0)))))) -> c16(MARK(adx(tl(incr(tl(y0)))))) MARK(hd(adx(tl(incr(cons(y0, y1)))))) -> c16(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(hd(adx(tl(incr(s(y0)))))) -> c16(MARK(adx(tl(incr(s(y0)))))) MARK(hd(adx(tl(incr(y0))))) -> c16(MARK(adx(tl(incr(y0))))) MARK(hd(adx(tl(hd(nats))))) -> c16(MARK(adx(tl(hd(nats))))) MARK(hd(adx(tl(hd(adx(y0)))))) -> c16(MARK(adx(tl(hd(adx(y0)))))) MARK(hd(adx(tl(hd(incr(y0)))))) -> c16(MARK(adx(tl(hd(incr(y0)))))) MARK(hd(adx(tl(hd(hd(y0)))))) -> c16(MARK(adx(tl(hd(hd(y0)))))) MARK(hd(adx(tl(hd(tl(y0)))))) -> c16(MARK(adx(tl(hd(tl(y0)))))) MARK(hd(adx(tl(hd(cons(y0, y1)))))) -> c16(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(hd(adx(tl(hd(y0))))) -> c16(MARK(adx(tl(hd(y0))))) MARK(hd(adx(tl(tl(nats))))) -> c16(MARK(adx(tl(tl(nats))))) MARK(hd(adx(tl(tl(adx(y0)))))) -> c16(MARK(adx(tl(tl(adx(y0)))))) MARK(hd(adx(tl(tl(incr(y0)))))) -> c16(MARK(adx(tl(tl(incr(y0)))))) MARK(hd(adx(tl(tl(hd(y0)))))) -> c16(MARK(adx(tl(tl(hd(y0)))))) MARK(hd(adx(tl(tl(tl(y0)))))) -> c16(MARK(adx(tl(tl(tl(y0)))))) MARK(hd(adx(tl(tl(cons(y0, y1)))))) -> c16(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(hd(adx(tl(tl(y0))))) -> c16(MARK(adx(tl(tl(y0))))) MARK(hd(adx(tl(nats)))) -> c16(MARK(adx(tl(nats)))) MARK(hd(adx(hd(adx(0))))) -> c16(MARK(adx(hd(adx(0))))) MARK(hd(adx(hd(adx(s(y0)))))) -> c16(MARK(adx(hd(adx(s(y0)))))) MARK(hd(adx(hd(incr(0))))) -> c16(MARK(adx(hd(incr(0))))) MARK(hd(adx(hd(incr(s(y0)))))) -> c16(MARK(adx(hd(incr(s(y0)))))) MARK(hd(adx(hd(hd(zeros))))) -> c16(MARK(adx(hd(hd(zeros))))) MARK(hd(adx(tl(hd(zeros))))) -> c16(MARK(adx(tl(hd(zeros))))) MARK(hd(adx(tl(adx(0))))) -> c16(MARK(adx(tl(adx(0))))) MARK(hd(adx(hd(tl(zeros))))) -> c16(MARK(adx(hd(tl(zeros))))) MARK(hd(adx(tl(tl(zeros))))) -> c16(MARK(adx(tl(tl(zeros))))) MARK(hd(adx(tl(adx(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) MARK(hd(adx(tl(incr(0))))) -> c16(MARK(adx(tl(incr(0))))) MARK(hd(incr(incr(y0)))) -> c16(MARK(incr(incr(y0)))) MARK(hd(incr(hd(cons(y0, y1))))) -> c16(MARK(incr(hd(cons(y0, y1))))) MARK(hd(incr(tl(cons(y0, y1))))) -> c16(MARK(incr(tl(cons(y0, y1))))) MARK(hd(incr(hd(adx(adx(y0)))))) -> c16(MARK(incr(hd(adx(adx(y0)))))) MARK(hd(incr(hd(adx(incr(y0)))))) -> c16(MARK(incr(hd(adx(incr(y0)))))) MARK(hd(incr(hd(adx(hd(y0)))))) -> c16(MARK(incr(hd(adx(hd(y0)))))) MARK(hd(incr(hd(adx(tl(y0)))))) -> c16(MARK(incr(hd(adx(tl(y0)))))) MARK(hd(incr(hd(adx(y0))))) -> c16(MARK(incr(hd(adx(y0))))) MARK(hd(incr(hd(incr(nats))))) -> c16(MARK(incr(hd(incr(nats))))) MARK(hd(incr(hd(incr(adx(y0)))))) -> c16(MARK(incr(hd(incr(adx(y0)))))) MARK(hd(incr(hd(incr(zeros))))) -> c16(MARK(incr(hd(incr(zeros))))) MARK(hd(incr(hd(incr(incr(y0)))))) -> c16(MARK(incr(hd(incr(incr(y0)))))) MARK(hd(incr(hd(incr(hd(y0)))))) -> c16(MARK(incr(hd(incr(hd(y0)))))) MARK(hd(incr(hd(incr(tl(y0)))))) -> c16(MARK(incr(hd(incr(tl(y0)))))) MARK(hd(incr(hd(incr(cons(y0, y1)))))) -> c16(MARK(incr(hd(incr(cons(y0, y1)))))) MARK(hd(incr(hd(incr(y0))))) -> c16(MARK(incr(hd(incr(y0))))) MARK(hd(incr(hd(hd(nats))))) -> c16(MARK(incr(hd(hd(nats))))) MARK(hd(incr(hd(hd(adx(y0)))))) -> c16(MARK(incr(hd(hd(adx(y0)))))) MARK(hd(incr(hd(hd(incr(y0)))))) -> c16(MARK(incr(hd(hd(incr(y0)))))) MARK(hd(incr(hd(hd(hd(y0)))))) -> c16(MARK(incr(hd(hd(hd(y0)))))) MARK(hd(incr(hd(hd(tl(y0)))))) -> c16(MARK(incr(hd(hd(tl(y0)))))) MARK(hd(incr(hd(hd(cons(y0, y1)))))) -> c16(MARK(incr(hd(hd(cons(y0, y1)))))) MARK(hd(incr(hd(hd(y0))))) -> c16(MARK(incr(hd(hd(y0))))) MARK(hd(incr(hd(tl(nats))))) -> c16(MARK(incr(hd(tl(nats))))) MARK(hd(incr(hd(tl(adx(y0)))))) -> c16(MARK(incr(hd(tl(adx(y0)))))) MARK(hd(incr(hd(tl(incr(y0)))))) -> c16(MARK(incr(hd(tl(incr(y0)))))) MARK(hd(incr(hd(tl(hd(y0)))))) -> c16(MARK(incr(hd(tl(hd(y0)))))) MARK(hd(incr(hd(tl(tl(y0)))))) -> c16(MARK(incr(hd(tl(tl(y0)))))) MARK(hd(incr(hd(tl(cons(y0, y1)))))) -> c16(MARK(incr(hd(tl(cons(y0, y1)))))) MARK(hd(incr(hd(tl(y0))))) -> c16(MARK(incr(hd(tl(y0))))) MARK(hd(incr(hd(nats)))) -> c16(MARK(incr(hd(nats)))) MARK(hd(incr(tl(adx(adx(y0)))))) -> c16(MARK(incr(tl(adx(adx(y0)))))) MARK(hd(incr(tl(adx(incr(y0)))))) -> c16(MARK(incr(tl(adx(incr(y0)))))) MARK(hd(incr(tl(adx(hd(y0)))))) -> c16(MARK(incr(tl(adx(hd(y0)))))) MARK(hd(incr(tl(adx(tl(y0)))))) -> c16(MARK(incr(tl(adx(tl(y0)))))) MARK(hd(incr(tl(adx(y0))))) -> c16(MARK(incr(tl(adx(y0))))) MARK(hd(incr(tl(incr(nats))))) -> c16(MARK(incr(tl(incr(nats))))) MARK(hd(incr(tl(incr(adx(y0)))))) -> c16(MARK(incr(tl(incr(adx(y0)))))) MARK(hd(incr(tl(incr(zeros))))) -> c16(MARK(incr(tl(incr(zeros))))) MARK(hd(incr(tl(incr(incr(y0)))))) -> c16(MARK(incr(tl(incr(incr(y0)))))) MARK(hd(incr(tl(incr(hd(y0)))))) -> c16(MARK(incr(tl(incr(hd(y0)))))) MARK(hd(incr(tl(incr(tl(y0)))))) -> c16(MARK(incr(tl(incr(tl(y0)))))) MARK(hd(incr(tl(incr(cons(y0, y1)))))) -> c16(MARK(incr(tl(incr(cons(y0, y1)))))) MARK(hd(incr(tl(incr(y0))))) -> c16(MARK(incr(tl(incr(y0))))) MARK(hd(incr(tl(hd(nats))))) -> c16(MARK(incr(tl(hd(nats))))) MARK(hd(incr(tl(hd(adx(y0)))))) -> c16(MARK(incr(tl(hd(adx(y0)))))) MARK(hd(incr(tl(hd(incr(y0)))))) -> c16(MARK(incr(tl(hd(incr(y0)))))) MARK(hd(incr(tl(hd(hd(y0)))))) -> c16(MARK(incr(tl(hd(hd(y0)))))) MARK(hd(incr(tl(hd(tl(y0)))))) -> c16(MARK(incr(tl(hd(tl(y0)))))) MARK(hd(incr(tl(hd(cons(y0, y1)))))) -> c16(MARK(incr(tl(hd(cons(y0, y1)))))) MARK(hd(incr(tl(hd(y0))))) -> c16(MARK(incr(tl(hd(y0))))) MARK(hd(incr(tl(tl(nats))))) -> c16(MARK(incr(tl(tl(nats))))) MARK(hd(incr(tl(tl(adx(y0)))))) -> c16(MARK(incr(tl(tl(adx(y0)))))) MARK(hd(incr(tl(tl(incr(y0)))))) -> c16(MARK(incr(tl(tl(incr(y0)))))) MARK(hd(incr(tl(tl(hd(y0)))))) -> c16(MARK(incr(tl(tl(hd(y0)))))) MARK(hd(incr(tl(tl(tl(y0)))))) -> c16(MARK(incr(tl(tl(tl(y0)))))) MARK(hd(incr(tl(tl(cons(y0, y1)))))) -> c16(MARK(incr(tl(tl(cons(y0, y1)))))) MARK(hd(incr(tl(tl(y0))))) -> c16(MARK(incr(tl(tl(y0))))) MARK(hd(incr(tl(nats)))) -> c16(MARK(incr(tl(nats)))) MARK(hd(incr(hd(incr(0))))) -> c16(MARK(incr(hd(incr(0))))) MARK(hd(incr(hd(incr(s(y0)))))) -> c16(MARK(incr(hd(incr(s(y0)))))) MARK(hd(incr(hd(hd(zeros))))) -> c16(MARK(incr(hd(hd(zeros))))) MARK(hd(incr(tl(hd(zeros))))) -> c16(MARK(incr(tl(hd(zeros))))) MARK(hd(incr(hd(tl(zeros))))) -> c16(MARK(incr(hd(tl(zeros))))) MARK(hd(incr(tl(tl(zeros))))) -> c16(MARK(incr(tl(tl(zeros))))) MARK(hd(incr(tl(incr(0))))) -> c16(MARK(incr(tl(incr(0))))) MARK(hd(incr(adx(adx(y0))))) -> c16(MARK(incr(adx(adx(y0))))) MARK(hd(incr(adx(incr(y0))))) -> c16(MARK(incr(adx(incr(y0))))) MARK(hd(incr(adx(hd(cons(y0, y1)))))) -> c16(MARK(incr(adx(hd(cons(y0, y1)))))) MARK(hd(incr(adx(tl(cons(y0, y1)))))) -> c16(MARK(incr(adx(tl(cons(y0, y1)))))) MARK(hd(incr(adx(hd(adx(nats)))))) -> c16(MARK(incr(adx(hd(adx(nats)))))) MARK(hd(incr(adx(hd(adx(adx(y0))))))) -> c16(MARK(incr(adx(hd(adx(adx(y0))))))) MARK(hd(incr(adx(hd(adx(zeros)))))) -> c16(MARK(incr(adx(hd(adx(zeros)))))) MARK(hd(incr(adx(hd(adx(incr(y0))))))) -> c16(MARK(incr(adx(hd(adx(incr(y0))))))) MARK(hd(incr(adx(hd(adx(hd(y0))))))) -> c16(MARK(incr(adx(hd(adx(hd(y0))))))) MARK(hd(incr(adx(hd(adx(tl(y0))))))) -> c16(MARK(incr(adx(hd(adx(tl(y0))))))) MARK(hd(incr(adx(hd(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(adx(cons(y0, y1))))))) MARK(hd(incr(adx(hd(adx(y0)))))) -> c16(MARK(incr(adx(hd(adx(y0)))))) MARK(hd(incr(adx(hd(incr(nats)))))) -> c16(MARK(incr(adx(hd(incr(nats)))))) MARK(hd(incr(adx(hd(incr(adx(y0))))))) -> c16(MARK(incr(adx(hd(incr(adx(y0))))))) MARK(hd(incr(adx(hd(incr(zeros)))))) -> c16(MARK(incr(adx(hd(incr(zeros)))))) MARK(hd(incr(adx(hd(incr(incr(y0))))))) -> c16(MARK(incr(adx(hd(incr(incr(y0))))))) MARK(hd(incr(adx(hd(incr(hd(y0))))))) -> c16(MARK(incr(adx(hd(incr(hd(y0))))))) MARK(hd(incr(adx(hd(incr(tl(y0))))))) -> c16(MARK(incr(adx(hd(incr(tl(y0))))))) MARK(hd(incr(adx(hd(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(incr(cons(y0, y1))))))) MARK(hd(incr(adx(hd(incr(y0)))))) -> c16(MARK(incr(adx(hd(incr(y0)))))) MARK(hd(incr(adx(hd(hd(nats)))))) -> c16(MARK(incr(adx(hd(hd(nats)))))) MARK(hd(incr(adx(hd(hd(adx(y0))))))) -> c16(MARK(incr(adx(hd(hd(adx(y0))))))) MARK(hd(incr(adx(hd(hd(incr(y0))))))) -> c16(MARK(incr(adx(hd(hd(incr(y0))))))) MARK(hd(incr(adx(hd(hd(hd(y0))))))) -> c16(MARK(incr(adx(hd(hd(hd(y0))))))) MARK(hd(incr(adx(hd(hd(tl(y0))))))) -> c16(MARK(incr(adx(hd(hd(tl(y0))))))) MARK(hd(incr(adx(hd(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(hd(cons(y0, y1))))))) MARK(hd(incr(adx(hd(hd(y0)))))) -> c16(MARK(incr(adx(hd(hd(y0)))))) MARK(hd(incr(adx(hd(tl(nats)))))) -> c16(MARK(incr(adx(hd(tl(nats)))))) MARK(hd(incr(adx(hd(tl(adx(y0))))))) -> c16(MARK(incr(adx(hd(tl(adx(y0))))))) MARK(hd(incr(adx(hd(tl(incr(y0))))))) -> c16(MARK(incr(adx(hd(tl(incr(y0))))))) MARK(hd(incr(adx(hd(tl(hd(y0))))))) -> c16(MARK(incr(adx(hd(tl(hd(y0))))))) MARK(hd(incr(adx(hd(tl(tl(y0))))))) -> c16(MARK(incr(adx(hd(tl(tl(y0))))))) MARK(hd(incr(adx(hd(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(tl(cons(y0, y1))))))) MARK(hd(incr(adx(hd(tl(y0)))))) -> c16(MARK(incr(adx(hd(tl(y0)))))) MARK(hd(incr(adx(hd(nats))))) -> c16(MARK(incr(adx(hd(nats))))) MARK(hd(incr(adx(tl(adx(nats)))))) -> c16(MARK(incr(adx(tl(adx(nats)))))) MARK(hd(incr(adx(tl(adx(adx(y0))))))) -> c16(MARK(incr(adx(tl(adx(adx(y0))))))) MARK(hd(incr(adx(tl(adx(zeros)))))) -> c16(MARK(incr(adx(tl(adx(zeros)))))) MARK(hd(incr(adx(tl(adx(incr(y0))))))) -> c16(MARK(incr(adx(tl(adx(incr(y0))))))) MARK(hd(incr(adx(tl(adx(hd(y0))))))) -> c16(MARK(incr(adx(tl(adx(hd(y0))))))) MARK(hd(incr(adx(tl(adx(tl(y0))))))) -> c16(MARK(incr(adx(tl(adx(tl(y0))))))) MARK(hd(incr(adx(tl(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(adx(cons(y0, y1))))))) MARK(hd(incr(adx(tl(adx(y0)))))) -> c16(MARK(incr(adx(tl(adx(y0)))))) MARK(hd(incr(adx(tl(incr(nats)))))) -> c16(MARK(incr(adx(tl(incr(nats)))))) MARK(hd(incr(adx(tl(incr(adx(y0))))))) -> c16(MARK(incr(adx(tl(incr(adx(y0))))))) MARK(hd(incr(adx(tl(incr(zeros)))))) -> c16(MARK(incr(adx(tl(incr(zeros)))))) MARK(hd(incr(adx(tl(incr(incr(y0))))))) -> c16(MARK(incr(adx(tl(incr(incr(y0))))))) MARK(hd(incr(adx(tl(incr(hd(y0))))))) -> c16(MARK(incr(adx(tl(incr(hd(y0))))))) MARK(hd(incr(adx(tl(incr(tl(y0))))))) -> c16(MARK(incr(adx(tl(incr(tl(y0))))))) MARK(hd(incr(adx(tl(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(incr(cons(y0, y1))))))) MARK(hd(incr(adx(tl(incr(s(y0))))))) -> c16(MARK(incr(adx(tl(incr(s(y0))))))) MARK(hd(incr(adx(tl(incr(y0)))))) -> c16(MARK(incr(adx(tl(incr(y0)))))) MARK(hd(incr(adx(tl(hd(nats)))))) -> c16(MARK(incr(adx(tl(hd(nats)))))) MARK(hd(incr(adx(tl(hd(adx(y0))))))) -> c16(MARK(incr(adx(tl(hd(adx(y0))))))) MARK(hd(incr(adx(tl(hd(incr(y0))))))) -> c16(MARK(incr(adx(tl(hd(incr(y0))))))) MARK(hd(incr(adx(tl(hd(hd(y0))))))) -> c16(MARK(incr(adx(tl(hd(hd(y0))))))) MARK(hd(incr(adx(tl(hd(tl(y0))))))) -> c16(MARK(incr(adx(tl(hd(tl(y0))))))) MARK(hd(incr(adx(tl(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(hd(cons(y0, y1))))))) MARK(hd(incr(adx(tl(hd(y0)))))) -> c16(MARK(incr(adx(tl(hd(y0)))))) MARK(hd(incr(adx(tl(tl(nats)))))) -> c16(MARK(incr(adx(tl(tl(nats)))))) MARK(hd(incr(adx(tl(tl(adx(y0))))))) -> c16(MARK(incr(adx(tl(tl(adx(y0))))))) MARK(hd(incr(adx(tl(tl(incr(y0))))))) -> c16(MARK(incr(adx(tl(tl(incr(y0))))))) MARK(hd(incr(adx(tl(tl(hd(y0))))))) -> c16(MARK(incr(adx(tl(tl(hd(y0))))))) MARK(hd(incr(adx(tl(tl(tl(y0))))))) -> c16(MARK(incr(adx(tl(tl(tl(y0))))))) MARK(hd(incr(adx(tl(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(tl(cons(y0, y1))))))) MARK(hd(incr(adx(tl(tl(y0)))))) -> c16(MARK(incr(adx(tl(tl(y0)))))) MARK(hd(incr(adx(tl(nats))))) -> c16(MARK(incr(adx(tl(nats))))) MARK(hd(incr(adx(hd(adx(0)))))) -> c16(MARK(incr(adx(hd(adx(0)))))) MARK(hd(incr(adx(hd(adx(s(y0))))))) -> c16(MARK(incr(adx(hd(adx(s(y0))))))) MARK(hd(incr(adx(hd(incr(0)))))) -> c16(MARK(incr(adx(hd(incr(0)))))) MARK(hd(incr(adx(hd(incr(s(y0))))))) -> c16(MARK(incr(adx(hd(incr(s(y0))))))) MARK(hd(incr(adx(hd(hd(zeros)))))) -> c16(MARK(incr(adx(hd(hd(zeros)))))) MARK(hd(incr(adx(tl(hd(zeros)))))) -> c16(MARK(incr(adx(tl(hd(zeros)))))) MARK(hd(incr(adx(tl(adx(0)))))) -> c16(MARK(incr(adx(tl(adx(0)))))) MARK(hd(incr(adx(hd(tl(zeros)))))) -> c16(MARK(incr(adx(hd(tl(zeros)))))) MARK(hd(incr(adx(tl(tl(zeros)))))) -> c16(MARK(incr(adx(tl(tl(zeros)))))) MARK(hd(incr(adx(tl(adx(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) MARK(hd(incr(adx(tl(incr(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) MARK(hd(incr(hd(adx(nats))))) -> c16(MARK(incr(hd(adx(nats))))) MARK(hd(incr(hd(adx(zeros))))) -> c16(MARK(incr(hd(adx(zeros))))) MARK(hd(incr(hd(adx(cons(y0, y1)))))) -> c16(MARK(incr(hd(adx(cons(y0, y1)))))) MARK(hd(incr(tl(adx(nats))))) -> c16(MARK(incr(tl(adx(nats))))) MARK(hd(incr(tl(adx(zeros))))) -> c16(MARK(incr(tl(adx(zeros))))) MARK(hd(incr(tl(adx(cons(y0, y1)))))) -> c16(MARK(incr(tl(adx(cons(y0, y1)))))) MARK(hd(incr(tl(incr(s(y0)))))) -> c16(MARK(incr(tl(incr(s(y0)))))) S tuples: MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) MARK(tl(cons(z0, adx(y1)))) -> c17(A__TL(cons(z0, adx(y1)))) MARK(tl(cons(z0, incr(y1)))) -> c17(A__TL(cons(z0, incr(y1)))) MARK(tl(cons(z0, hd(cons(y1, y2))))) -> c17(A__TL(cons(z0, hd(cons(y1, y2))))) MARK(tl(cons(z0, tl(cons(y1, y2))))) -> c17(A__TL(cons(z0, tl(cons(y1, y2))))) MARK(tl(cons(z0, hd(adx(nats))))) -> c17(A__TL(cons(z0, hd(adx(nats))))) MARK(tl(cons(z0, hd(adx(adx(y1)))))) -> c17(A__TL(cons(z0, hd(adx(adx(y1)))))) MARK(tl(cons(z0, hd(adx(zeros))))) -> c17(A__TL(cons(z0, hd(adx(zeros))))) MARK(tl(cons(z0, hd(adx(incr(y1)))))) -> c17(A__TL(cons(z0, hd(adx(incr(y1)))))) MARK(tl(cons(z0, hd(adx(hd(y1)))))) -> c17(A__TL(cons(z0, hd(adx(hd(y1)))))) MARK(tl(cons(z0, hd(adx(tl(y1)))))) -> c17(A__TL(cons(z0, hd(adx(tl(y1)))))) MARK(tl(cons(z0, hd(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(adx(cons(y1, y2)))))) MARK(tl(cons(z0, hd(adx(y1))))) -> c17(A__TL(cons(z0, hd(adx(y1))))) MARK(tl(cons(z0, hd(incr(nats))))) -> c17(A__TL(cons(z0, hd(incr(nats))))) MARK(tl(cons(z0, hd(incr(adx(y1)))))) -> c17(A__TL(cons(z0, hd(incr(adx(y1)))))) MARK(tl(cons(z0, hd(incr(zeros))))) -> c17(A__TL(cons(z0, hd(incr(zeros))))) MARK(tl(cons(z0, hd(incr(incr(y1)))))) -> c17(A__TL(cons(z0, hd(incr(incr(y1)))))) MARK(tl(cons(z0, hd(incr(hd(y1)))))) -> c17(A__TL(cons(z0, hd(incr(hd(y1)))))) MARK(tl(cons(z0, hd(incr(tl(y1)))))) -> c17(A__TL(cons(z0, hd(incr(tl(y1)))))) MARK(tl(cons(z0, hd(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(incr(cons(y1, y2)))))) MARK(tl(cons(z0, hd(incr(y1))))) -> c17(A__TL(cons(z0, hd(incr(y1))))) MARK(tl(cons(z0, hd(hd(nats))))) -> c17(A__TL(cons(z0, hd(hd(nats))))) MARK(tl(cons(z0, hd(hd(adx(y1)))))) -> c17(A__TL(cons(z0, hd(hd(adx(y1)))))) MARK(tl(cons(z0, hd(hd(incr(y1)))))) -> c17(A__TL(cons(z0, hd(hd(incr(y1)))))) MARK(tl(cons(z0, hd(hd(hd(y1)))))) -> c17(A__TL(cons(z0, hd(hd(hd(y1)))))) MARK(tl(cons(z0, hd(hd(tl(y1)))))) -> c17(A__TL(cons(z0, hd(hd(tl(y1)))))) MARK(tl(cons(z0, hd(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(hd(cons(y1, y2)))))) MARK(tl(cons(z0, hd(hd(y1))))) -> c17(A__TL(cons(z0, hd(hd(y1))))) MARK(tl(cons(z0, hd(tl(nats))))) -> c17(A__TL(cons(z0, hd(tl(nats))))) MARK(tl(cons(z0, hd(tl(adx(y1)))))) -> c17(A__TL(cons(z0, hd(tl(adx(y1)))))) MARK(tl(cons(z0, hd(tl(zeros))))) -> c17(A__TL(cons(z0, hd(tl(zeros))))) MARK(tl(cons(z0, hd(tl(incr(y1)))))) -> c17(A__TL(cons(z0, hd(tl(incr(y1)))))) MARK(tl(cons(z0, hd(tl(hd(y1)))))) -> c17(A__TL(cons(z0, hd(tl(hd(y1)))))) MARK(tl(cons(z0, hd(tl(tl(y1)))))) -> c17(A__TL(cons(z0, hd(tl(tl(y1)))))) MARK(tl(cons(z0, hd(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(tl(cons(y1, y2)))))) MARK(tl(cons(z0, hd(tl(y1))))) -> c17(A__TL(cons(z0, hd(tl(y1))))) MARK(tl(cons(z0, hd(nats)))) -> c17(A__TL(cons(z0, hd(nats)))) MARK(tl(cons(z0, tl(adx(nats))))) -> c17(A__TL(cons(z0, tl(adx(nats))))) MARK(tl(cons(z0, tl(adx(adx(y1)))))) -> c17(A__TL(cons(z0, tl(adx(adx(y1)))))) MARK(tl(cons(z0, tl(adx(zeros))))) -> c17(A__TL(cons(z0, tl(adx(zeros))))) MARK(tl(cons(z0, tl(adx(incr(y1)))))) -> c17(A__TL(cons(z0, tl(adx(incr(y1)))))) MARK(tl(cons(z0, tl(adx(hd(y1)))))) -> c17(A__TL(cons(z0, tl(adx(hd(y1)))))) MARK(tl(cons(z0, tl(adx(tl(y1)))))) -> c17(A__TL(cons(z0, tl(adx(tl(y1)))))) MARK(tl(cons(z0, tl(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(adx(cons(y1, y2)))))) MARK(tl(cons(z0, tl(adx(s(y1)))))) -> c17(A__TL(cons(z0, tl(adx(s(y1)))))) MARK(tl(cons(z0, tl(adx(y1))))) -> c17(A__TL(cons(z0, tl(adx(y1))))) MARK(tl(cons(z0, tl(incr(nats))))) -> c17(A__TL(cons(z0, tl(incr(nats))))) MARK(tl(cons(z0, tl(incr(adx(y1)))))) -> c17(A__TL(cons(z0, tl(incr(adx(y1)))))) MARK(tl(cons(z0, tl(incr(zeros))))) -> c17(A__TL(cons(z0, tl(incr(zeros))))) MARK(tl(cons(z0, tl(incr(incr(y1)))))) -> c17(A__TL(cons(z0, tl(incr(incr(y1)))))) MARK(tl(cons(z0, tl(incr(hd(y1)))))) -> c17(A__TL(cons(z0, tl(incr(hd(y1)))))) MARK(tl(cons(z0, tl(incr(tl(y1)))))) -> c17(A__TL(cons(z0, tl(incr(tl(y1)))))) MARK(tl(cons(z0, tl(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(incr(cons(y1, y2)))))) MARK(tl(cons(z0, tl(incr(0))))) -> c17(A__TL(cons(z0, tl(incr(0))))) MARK(tl(cons(z0, tl(incr(s(y1)))))) -> c17(A__TL(cons(z0, tl(incr(s(y1)))))) MARK(tl(cons(z0, tl(incr(y1))))) -> c17(A__TL(cons(z0, tl(incr(y1))))) MARK(tl(cons(z0, tl(hd(nats))))) -> c17(A__TL(cons(z0, tl(hd(nats))))) MARK(tl(cons(z0, tl(hd(adx(y1)))))) -> c17(A__TL(cons(z0, tl(hd(adx(y1)))))) MARK(tl(cons(z0, tl(hd(incr(y1)))))) -> c17(A__TL(cons(z0, tl(hd(incr(y1)))))) MARK(tl(cons(z0, tl(hd(hd(y1)))))) -> c17(A__TL(cons(z0, tl(hd(hd(y1)))))) MARK(tl(cons(z0, tl(hd(tl(y1)))))) -> c17(A__TL(cons(z0, tl(hd(tl(y1)))))) MARK(tl(cons(z0, tl(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(hd(cons(y1, y2)))))) MARK(tl(cons(z0, tl(hd(y1))))) -> c17(A__TL(cons(z0, tl(hd(y1))))) MARK(tl(cons(z0, tl(tl(nats))))) -> c17(A__TL(cons(z0, tl(tl(nats))))) MARK(tl(cons(z0, tl(tl(adx(y1)))))) -> c17(A__TL(cons(z0, tl(tl(adx(y1)))))) MARK(tl(cons(z0, tl(tl(zeros))))) -> c17(A__TL(cons(z0, tl(tl(zeros))))) MARK(tl(cons(z0, tl(tl(incr(y1)))))) -> c17(A__TL(cons(z0, tl(tl(incr(y1)))))) MARK(tl(cons(z0, tl(tl(hd(y1)))))) -> c17(A__TL(cons(z0, tl(tl(hd(y1)))))) MARK(tl(cons(z0, tl(tl(tl(y1)))))) -> c17(A__TL(cons(z0, tl(tl(tl(y1)))))) MARK(tl(cons(z0, tl(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(tl(cons(y1, y2)))))) MARK(tl(cons(z0, tl(tl(y1))))) -> c17(A__TL(cons(z0, tl(tl(y1))))) MARK(tl(cons(z0, tl(nats)))) -> c17(A__TL(cons(z0, tl(nats)))) MARK(tl(cons(z0, hd(adx(0))))) -> c17(A__TL(cons(z0, hd(adx(0))))) MARK(tl(cons(z0, hd(adx(s(y1)))))) -> c17(A__TL(cons(z0, hd(adx(s(y1)))))) MARK(tl(cons(z0, hd(incr(0))))) -> c17(A__TL(cons(z0, hd(incr(0))))) MARK(tl(cons(z0, hd(incr(s(y1)))))) -> c17(A__TL(cons(z0, hd(incr(s(y1)))))) MARK(tl(cons(z0, hd(hd(zeros))))) -> c17(A__TL(cons(z0, hd(hd(zeros))))) MARK(tl(cons(z0, tl(hd(zeros))))) -> c17(A__TL(cons(z0, tl(hd(zeros))))) MARK(tl(cons(z0, tl(adx(0))))) -> c17(A__TL(cons(z0, tl(adx(0))))) MARK(hd(adx(adx(y0)))) -> c16(MARK(adx(adx(y0)))) MARK(hd(adx(incr(y0)))) -> c16(MARK(adx(incr(y0)))) MARK(hd(adx(hd(cons(y0, y1))))) -> c16(MARK(adx(hd(cons(y0, y1))))) MARK(hd(adx(tl(cons(y0, y1))))) -> c16(MARK(adx(tl(cons(y0, y1))))) MARK(hd(adx(hd(adx(nats))))) -> c16(MARK(adx(hd(adx(nats))))) MARK(hd(adx(hd(adx(adx(y0)))))) -> c16(MARK(adx(hd(adx(adx(y0)))))) MARK(hd(adx(hd(adx(zeros))))) -> c16(MARK(adx(hd(adx(zeros))))) MARK(hd(adx(hd(adx(incr(y0)))))) -> c16(MARK(adx(hd(adx(incr(y0)))))) MARK(hd(adx(hd(adx(hd(y0)))))) -> c16(MARK(adx(hd(adx(hd(y0)))))) MARK(hd(adx(hd(adx(tl(y0)))))) -> c16(MARK(adx(hd(adx(tl(y0)))))) MARK(hd(adx(hd(adx(cons(y0, y1)))))) -> c16(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(hd(adx(hd(adx(y0))))) -> c16(MARK(adx(hd(adx(y0))))) MARK(hd(adx(hd(incr(nats))))) -> c16(MARK(adx(hd(incr(nats))))) MARK(hd(adx(hd(incr(adx(y0)))))) -> c16(MARK(adx(hd(incr(adx(y0)))))) MARK(hd(adx(hd(incr(zeros))))) -> c16(MARK(adx(hd(incr(zeros))))) MARK(hd(adx(hd(incr(incr(y0)))))) -> c16(MARK(adx(hd(incr(incr(y0)))))) MARK(hd(adx(hd(incr(hd(y0)))))) -> c16(MARK(adx(hd(incr(hd(y0)))))) MARK(hd(adx(hd(incr(tl(y0)))))) -> c16(MARK(adx(hd(incr(tl(y0)))))) MARK(hd(adx(hd(incr(cons(y0, y1)))))) -> c16(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(hd(adx(hd(incr(y0))))) -> c16(MARK(adx(hd(incr(y0))))) MARK(hd(adx(hd(hd(nats))))) -> c16(MARK(adx(hd(hd(nats))))) MARK(hd(adx(hd(hd(adx(y0)))))) -> c16(MARK(adx(hd(hd(adx(y0)))))) MARK(hd(adx(hd(hd(incr(y0)))))) -> c16(MARK(adx(hd(hd(incr(y0)))))) MARK(hd(adx(hd(hd(hd(y0)))))) -> c16(MARK(adx(hd(hd(hd(y0)))))) MARK(hd(adx(hd(hd(tl(y0)))))) -> c16(MARK(adx(hd(hd(tl(y0)))))) MARK(hd(adx(hd(hd(cons(y0, y1)))))) -> c16(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(hd(adx(hd(hd(y0))))) -> c16(MARK(adx(hd(hd(y0))))) MARK(hd(adx(hd(tl(nats))))) -> c16(MARK(adx(hd(tl(nats))))) MARK(hd(adx(hd(tl(adx(y0)))))) -> c16(MARK(adx(hd(tl(adx(y0)))))) MARK(hd(adx(hd(tl(incr(y0)))))) -> c16(MARK(adx(hd(tl(incr(y0)))))) MARK(hd(adx(hd(tl(hd(y0)))))) -> c16(MARK(adx(hd(tl(hd(y0)))))) MARK(hd(adx(hd(tl(tl(y0)))))) -> c16(MARK(adx(hd(tl(tl(y0)))))) MARK(hd(adx(hd(tl(cons(y0, y1)))))) -> c16(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(hd(adx(hd(tl(y0))))) -> c16(MARK(adx(hd(tl(y0))))) MARK(hd(adx(hd(nats)))) -> c16(MARK(adx(hd(nats)))) MARK(hd(adx(tl(adx(nats))))) -> c16(MARK(adx(tl(adx(nats))))) MARK(hd(adx(tl(adx(adx(y0)))))) -> c16(MARK(adx(tl(adx(adx(y0)))))) MARK(hd(adx(tl(adx(zeros))))) -> c16(MARK(adx(tl(adx(zeros))))) MARK(hd(adx(tl(adx(incr(y0)))))) -> c16(MARK(adx(tl(adx(incr(y0)))))) MARK(hd(adx(tl(adx(hd(y0)))))) -> c16(MARK(adx(tl(adx(hd(y0)))))) MARK(hd(adx(tl(adx(tl(y0)))))) -> c16(MARK(adx(tl(adx(tl(y0)))))) MARK(hd(adx(tl(adx(cons(y0, y1)))))) -> c16(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(hd(adx(tl(adx(y0))))) -> c16(MARK(adx(tl(adx(y0))))) MARK(hd(adx(tl(incr(nats))))) -> c16(MARK(adx(tl(incr(nats))))) MARK(hd(adx(tl(incr(adx(y0)))))) -> c16(MARK(adx(tl(incr(adx(y0)))))) MARK(hd(adx(tl(incr(zeros))))) -> c16(MARK(adx(tl(incr(zeros))))) MARK(hd(adx(tl(incr(incr(y0)))))) -> c16(MARK(adx(tl(incr(incr(y0)))))) MARK(hd(adx(tl(incr(hd(y0)))))) -> c16(MARK(adx(tl(incr(hd(y0)))))) MARK(hd(adx(tl(incr(tl(y0)))))) -> c16(MARK(adx(tl(incr(tl(y0)))))) MARK(hd(adx(tl(incr(cons(y0, y1)))))) -> c16(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(hd(adx(tl(incr(s(y0)))))) -> c16(MARK(adx(tl(incr(s(y0)))))) MARK(hd(adx(tl(incr(y0))))) -> c16(MARK(adx(tl(incr(y0))))) MARK(hd(adx(tl(hd(nats))))) -> c16(MARK(adx(tl(hd(nats))))) MARK(hd(adx(tl(hd(adx(y0)))))) -> c16(MARK(adx(tl(hd(adx(y0)))))) MARK(hd(adx(tl(hd(incr(y0)))))) -> c16(MARK(adx(tl(hd(incr(y0)))))) MARK(hd(adx(tl(hd(hd(y0)))))) -> c16(MARK(adx(tl(hd(hd(y0)))))) MARK(hd(adx(tl(hd(tl(y0)))))) -> c16(MARK(adx(tl(hd(tl(y0)))))) MARK(hd(adx(tl(hd(cons(y0, y1)))))) -> c16(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(hd(adx(tl(hd(y0))))) -> c16(MARK(adx(tl(hd(y0))))) MARK(hd(adx(tl(tl(nats))))) -> c16(MARK(adx(tl(tl(nats))))) MARK(hd(adx(tl(tl(adx(y0)))))) -> c16(MARK(adx(tl(tl(adx(y0)))))) MARK(hd(adx(tl(tl(incr(y0)))))) -> c16(MARK(adx(tl(tl(incr(y0)))))) MARK(hd(adx(tl(tl(hd(y0)))))) -> c16(MARK(adx(tl(tl(hd(y0)))))) MARK(hd(adx(tl(tl(tl(y0)))))) -> c16(MARK(adx(tl(tl(tl(y0)))))) MARK(hd(adx(tl(tl(cons(y0, y1)))))) -> c16(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(hd(adx(tl(tl(y0))))) -> c16(MARK(adx(tl(tl(y0))))) MARK(hd(adx(tl(nats)))) -> c16(MARK(adx(tl(nats)))) MARK(hd(adx(hd(adx(0))))) -> c16(MARK(adx(hd(adx(0))))) MARK(hd(adx(hd(adx(s(y0)))))) -> c16(MARK(adx(hd(adx(s(y0)))))) MARK(hd(adx(hd(incr(0))))) -> c16(MARK(adx(hd(incr(0))))) MARK(hd(adx(hd(incr(s(y0)))))) -> c16(MARK(adx(hd(incr(s(y0)))))) MARK(hd(adx(hd(hd(zeros))))) -> c16(MARK(adx(hd(hd(zeros))))) MARK(hd(adx(tl(hd(zeros))))) -> c16(MARK(adx(tl(hd(zeros))))) MARK(hd(adx(tl(adx(0))))) -> c16(MARK(adx(tl(adx(0))))) MARK(hd(adx(hd(tl(zeros))))) -> c16(MARK(adx(hd(tl(zeros))))) MARK(hd(adx(tl(tl(zeros))))) -> c16(MARK(adx(tl(tl(zeros))))) MARK(hd(adx(tl(adx(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) MARK(hd(adx(tl(incr(0))))) -> c16(MARK(adx(tl(incr(0))))) MARK(hd(incr(incr(y0)))) -> c16(MARK(incr(incr(y0)))) MARK(hd(incr(hd(cons(y0, y1))))) -> c16(MARK(incr(hd(cons(y0, y1))))) MARK(hd(incr(tl(cons(y0, y1))))) -> c16(MARK(incr(tl(cons(y0, y1))))) MARK(hd(incr(hd(adx(adx(y0)))))) -> c16(MARK(incr(hd(adx(adx(y0)))))) MARK(hd(incr(hd(adx(incr(y0)))))) -> c16(MARK(incr(hd(adx(incr(y0)))))) MARK(hd(incr(hd(adx(hd(y0)))))) -> c16(MARK(incr(hd(adx(hd(y0)))))) MARK(hd(incr(hd(adx(tl(y0)))))) -> c16(MARK(incr(hd(adx(tl(y0)))))) MARK(hd(incr(hd(adx(y0))))) -> c16(MARK(incr(hd(adx(y0))))) MARK(hd(incr(hd(incr(nats))))) -> c16(MARK(incr(hd(incr(nats))))) MARK(hd(incr(hd(incr(adx(y0)))))) -> c16(MARK(incr(hd(incr(adx(y0)))))) MARK(hd(incr(hd(incr(zeros))))) -> c16(MARK(incr(hd(incr(zeros))))) MARK(hd(incr(hd(incr(incr(y0)))))) -> c16(MARK(incr(hd(incr(incr(y0)))))) MARK(hd(incr(hd(incr(hd(y0)))))) -> c16(MARK(incr(hd(incr(hd(y0)))))) MARK(hd(incr(hd(incr(tl(y0)))))) -> c16(MARK(incr(hd(incr(tl(y0)))))) MARK(hd(incr(hd(incr(cons(y0, y1)))))) -> c16(MARK(incr(hd(incr(cons(y0, y1)))))) MARK(hd(incr(hd(incr(y0))))) -> c16(MARK(incr(hd(incr(y0))))) MARK(hd(incr(hd(hd(nats))))) -> c16(MARK(incr(hd(hd(nats))))) MARK(hd(incr(hd(hd(adx(y0)))))) -> c16(MARK(incr(hd(hd(adx(y0)))))) MARK(hd(incr(hd(hd(incr(y0)))))) -> c16(MARK(incr(hd(hd(incr(y0)))))) MARK(hd(incr(hd(hd(hd(y0)))))) -> c16(MARK(incr(hd(hd(hd(y0)))))) MARK(hd(incr(hd(hd(tl(y0)))))) -> c16(MARK(incr(hd(hd(tl(y0)))))) MARK(hd(incr(hd(hd(cons(y0, y1)))))) -> c16(MARK(incr(hd(hd(cons(y0, y1)))))) MARK(hd(incr(hd(hd(y0))))) -> c16(MARK(incr(hd(hd(y0))))) MARK(hd(incr(hd(tl(nats))))) -> c16(MARK(incr(hd(tl(nats))))) MARK(hd(incr(hd(tl(adx(y0)))))) -> c16(MARK(incr(hd(tl(adx(y0)))))) MARK(hd(incr(hd(tl(incr(y0)))))) -> c16(MARK(incr(hd(tl(incr(y0)))))) MARK(hd(incr(hd(tl(hd(y0)))))) -> c16(MARK(incr(hd(tl(hd(y0)))))) MARK(hd(incr(hd(tl(tl(y0)))))) -> c16(MARK(incr(hd(tl(tl(y0)))))) MARK(hd(incr(hd(tl(cons(y0, y1)))))) -> c16(MARK(incr(hd(tl(cons(y0, y1)))))) MARK(hd(incr(hd(tl(y0))))) -> c16(MARK(incr(hd(tl(y0))))) MARK(hd(incr(hd(nats)))) -> c16(MARK(incr(hd(nats)))) MARK(hd(incr(tl(adx(adx(y0)))))) -> c16(MARK(incr(tl(adx(adx(y0)))))) MARK(hd(incr(tl(adx(incr(y0)))))) -> c16(MARK(incr(tl(adx(incr(y0)))))) MARK(hd(incr(tl(adx(hd(y0)))))) -> c16(MARK(incr(tl(adx(hd(y0)))))) MARK(hd(incr(tl(adx(tl(y0)))))) -> c16(MARK(incr(tl(adx(tl(y0)))))) MARK(hd(incr(tl(adx(y0))))) -> c16(MARK(incr(tl(adx(y0))))) MARK(hd(incr(tl(incr(nats))))) -> c16(MARK(incr(tl(incr(nats))))) MARK(hd(incr(tl(incr(adx(y0)))))) -> c16(MARK(incr(tl(incr(adx(y0)))))) MARK(hd(incr(tl(incr(zeros))))) -> c16(MARK(incr(tl(incr(zeros))))) MARK(hd(incr(tl(incr(incr(y0)))))) -> c16(MARK(incr(tl(incr(incr(y0)))))) MARK(hd(incr(tl(incr(hd(y0)))))) -> c16(MARK(incr(tl(incr(hd(y0)))))) MARK(hd(incr(tl(incr(tl(y0)))))) -> c16(MARK(incr(tl(incr(tl(y0)))))) MARK(hd(incr(tl(incr(cons(y0, y1)))))) -> c16(MARK(incr(tl(incr(cons(y0, y1)))))) MARK(hd(incr(tl(incr(y0))))) -> c16(MARK(incr(tl(incr(y0))))) MARK(hd(incr(tl(hd(nats))))) -> c16(MARK(incr(tl(hd(nats))))) MARK(hd(incr(tl(hd(adx(y0)))))) -> c16(MARK(incr(tl(hd(adx(y0)))))) MARK(hd(incr(tl(hd(incr(y0)))))) -> c16(MARK(incr(tl(hd(incr(y0)))))) MARK(hd(incr(tl(hd(hd(y0)))))) -> c16(MARK(incr(tl(hd(hd(y0)))))) MARK(hd(incr(tl(hd(tl(y0)))))) -> c16(MARK(incr(tl(hd(tl(y0)))))) MARK(hd(incr(tl(hd(cons(y0, y1)))))) -> c16(MARK(incr(tl(hd(cons(y0, y1)))))) MARK(hd(incr(tl(hd(y0))))) -> c16(MARK(incr(tl(hd(y0))))) MARK(hd(incr(tl(tl(nats))))) -> c16(MARK(incr(tl(tl(nats))))) MARK(hd(incr(tl(tl(adx(y0)))))) -> c16(MARK(incr(tl(tl(adx(y0)))))) MARK(hd(incr(tl(tl(incr(y0)))))) -> c16(MARK(incr(tl(tl(incr(y0)))))) MARK(hd(incr(tl(tl(hd(y0)))))) -> c16(MARK(incr(tl(tl(hd(y0)))))) MARK(hd(incr(tl(tl(tl(y0)))))) -> c16(MARK(incr(tl(tl(tl(y0)))))) MARK(hd(incr(tl(tl(cons(y0, y1)))))) -> c16(MARK(incr(tl(tl(cons(y0, y1)))))) MARK(hd(incr(tl(tl(y0))))) -> c16(MARK(incr(tl(tl(y0))))) MARK(hd(incr(tl(nats)))) -> c16(MARK(incr(tl(nats)))) MARK(hd(incr(hd(incr(0))))) -> c16(MARK(incr(hd(incr(0))))) MARK(hd(incr(hd(incr(s(y0)))))) -> c16(MARK(incr(hd(incr(s(y0)))))) MARK(hd(incr(hd(hd(zeros))))) -> c16(MARK(incr(hd(hd(zeros))))) MARK(hd(incr(tl(hd(zeros))))) -> c16(MARK(incr(tl(hd(zeros))))) MARK(hd(incr(hd(tl(zeros))))) -> c16(MARK(incr(hd(tl(zeros))))) MARK(hd(incr(tl(tl(zeros))))) -> c16(MARK(incr(tl(tl(zeros))))) MARK(hd(incr(tl(incr(0))))) -> c16(MARK(incr(tl(incr(0))))) MARK(hd(incr(adx(adx(y0))))) -> c16(MARK(incr(adx(adx(y0))))) MARK(hd(incr(adx(incr(y0))))) -> c16(MARK(incr(adx(incr(y0))))) MARK(hd(incr(adx(hd(cons(y0, y1)))))) -> c16(MARK(incr(adx(hd(cons(y0, y1)))))) MARK(hd(incr(adx(tl(cons(y0, y1)))))) -> c16(MARK(incr(adx(tl(cons(y0, y1)))))) MARK(hd(incr(adx(hd(adx(nats)))))) -> c16(MARK(incr(adx(hd(adx(nats)))))) MARK(hd(incr(adx(hd(adx(adx(y0))))))) -> c16(MARK(incr(adx(hd(adx(adx(y0))))))) MARK(hd(incr(adx(hd(adx(zeros)))))) -> c16(MARK(incr(adx(hd(adx(zeros)))))) MARK(hd(incr(adx(hd(adx(incr(y0))))))) -> c16(MARK(incr(adx(hd(adx(incr(y0))))))) MARK(hd(incr(adx(hd(adx(hd(y0))))))) -> c16(MARK(incr(adx(hd(adx(hd(y0))))))) MARK(hd(incr(adx(hd(adx(tl(y0))))))) -> c16(MARK(incr(adx(hd(adx(tl(y0))))))) MARK(hd(incr(adx(hd(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(adx(cons(y0, y1))))))) MARK(hd(incr(adx(hd(adx(y0)))))) -> c16(MARK(incr(adx(hd(adx(y0)))))) MARK(hd(incr(adx(hd(incr(nats)))))) -> c16(MARK(incr(adx(hd(incr(nats)))))) MARK(hd(incr(adx(hd(incr(adx(y0))))))) -> c16(MARK(incr(adx(hd(incr(adx(y0))))))) MARK(hd(incr(adx(hd(incr(zeros)))))) -> c16(MARK(incr(adx(hd(incr(zeros)))))) MARK(hd(incr(adx(hd(incr(incr(y0))))))) -> c16(MARK(incr(adx(hd(incr(incr(y0))))))) MARK(hd(incr(adx(hd(incr(hd(y0))))))) -> c16(MARK(incr(adx(hd(incr(hd(y0))))))) MARK(hd(incr(adx(hd(incr(tl(y0))))))) -> c16(MARK(incr(adx(hd(incr(tl(y0))))))) MARK(hd(incr(adx(hd(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(incr(cons(y0, y1))))))) MARK(hd(incr(adx(hd(incr(y0)))))) -> c16(MARK(incr(adx(hd(incr(y0)))))) MARK(hd(incr(adx(hd(hd(nats)))))) -> c16(MARK(incr(adx(hd(hd(nats)))))) MARK(hd(incr(adx(hd(hd(adx(y0))))))) -> c16(MARK(incr(adx(hd(hd(adx(y0))))))) MARK(hd(incr(adx(hd(hd(incr(y0))))))) -> c16(MARK(incr(adx(hd(hd(incr(y0))))))) MARK(hd(incr(adx(hd(hd(hd(y0))))))) -> c16(MARK(incr(adx(hd(hd(hd(y0))))))) MARK(hd(incr(adx(hd(hd(tl(y0))))))) -> c16(MARK(incr(adx(hd(hd(tl(y0))))))) MARK(hd(incr(adx(hd(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(hd(cons(y0, y1))))))) MARK(hd(incr(adx(hd(hd(y0)))))) -> c16(MARK(incr(adx(hd(hd(y0)))))) MARK(hd(incr(adx(hd(tl(nats)))))) -> c16(MARK(incr(adx(hd(tl(nats)))))) MARK(hd(incr(adx(hd(tl(adx(y0))))))) -> c16(MARK(incr(adx(hd(tl(adx(y0))))))) MARK(hd(incr(adx(hd(tl(incr(y0))))))) -> c16(MARK(incr(adx(hd(tl(incr(y0))))))) MARK(hd(incr(adx(hd(tl(hd(y0))))))) -> c16(MARK(incr(adx(hd(tl(hd(y0))))))) MARK(hd(incr(adx(hd(tl(tl(y0))))))) -> c16(MARK(incr(adx(hd(tl(tl(y0))))))) MARK(hd(incr(adx(hd(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(tl(cons(y0, y1))))))) MARK(hd(incr(adx(hd(tl(y0)))))) -> c16(MARK(incr(adx(hd(tl(y0)))))) MARK(hd(incr(adx(hd(nats))))) -> c16(MARK(incr(adx(hd(nats))))) MARK(hd(incr(adx(tl(adx(nats)))))) -> c16(MARK(incr(adx(tl(adx(nats)))))) MARK(hd(incr(adx(tl(adx(adx(y0))))))) -> c16(MARK(incr(adx(tl(adx(adx(y0))))))) MARK(hd(incr(adx(tl(adx(zeros)))))) -> c16(MARK(incr(adx(tl(adx(zeros)))))) MARK(hd(incr(adx(tl(adx(incr(y0))))))) -> c16(MARK(incr(adx(tl(adx(incr(y0))))))) MARK(hd(incr(adx(tl(adx(hd(y0))))))) -> c16(MARK(incr(adx(tl(adx(hd(y0))))))) MARK(hd(incr(adx(tl(adx(tl(y0))))))) -> c16(MARK(incr(adx(tl(adx(tl(y0))))))) MARK(hd(incr(adx(tl(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(adx(cons(y0, y1))))))) MARK(hd(incr(adx(tl(adx(y0)))))) -> c16(MARK(incr(adx(tl(adx(y0)))))) MARK(hd(incr(adx(tl(incr(nats)))))) -> c16(MARK(incr(adx(tl(incr(nats)))))) MARK(hd(incr(adx(tl(incr(adx(y0))))))) -> c16(MARK(incr(adx(tl(incr(adx(y0))))))) MARK(hd(incr(adx(tl(incr(zeros)))))) -> c16(MARK(incr(adx(tl(incr(zeros)))))) MARK(hd(incr(adx(tl(incr(incr(y0))))))) -> c16(MARK(incr(adx(tl(incr(incr(y0))))))) MARK(hd(incr(adx(tl(incr(hd(y0))))))) -> c16(MARK(incr(adx(tl(incr(hd(y0))))))) MARK(hd(incr(adx(tl(incr(tl(y0))))))) -> c16(MARK(incr(adx(tl(incr(tl(y0))))))) MARK(hd(incr(adx(tl(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(incr(cons(y0, y1))))))) MARK(hd(incr(adx(tl(incr(s(y0))))))) -> c16(MARK(incr(adx(tl(incr(s(y0))))))) MARK(hd(incr(adx(tl(incr(y0)))))) -> c16(MARK(incr(adx(tl(incr(y0)))))) MARK(hd(incr(adx(tl(hd(nats)))))) -> c16(MARK(incr(adx(tl(hd(nats)))))) MARK(hd(incr(adx(tl(hd(adx(y0))))))) -> c16(MARK(incr(adx(tl(hd(adx(y0))))))) MARK(hd(incr(adx(tl(hd(incr(y0))))))) -> c16(MARK(incr(adx(tl(hd(incr(y0))))))) MARK(hd(incr(adx(tl(hd(hd(y0))))))) -> c16(MARK(incr(adx(tl(hd(hd(y0))))))) MARK(hd(incr(adx(tl(hd(tl(y0))))))) -> c16(MARK(incr(adx(tl(hd(tl(y0))))))) MARK(hd(incr(adx(tl(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(hd(cons(y0, y1))))))) MARK(hd(incr(adx(tl(hd(y0)))))) -> c16(MARK(incr(adx(tl(hd(y0)))))) MARK(hd(incr(adx(tl(tl(nats)))))) -> c16(MARK(incr(adx(tl(tl(nats)))))) MARK(hd(incr(adx(tl(tl(adx(y0))))))) -> c16(MARK(incr(adx(tl(tl(adx(y0))))))) MARK(hd(incr(adx(tl(tl(incr(y0))))))) -> c16(MARK(incr(adx(tl(tl(incr(y0))))))) MARK(hd(incr(adx(tl(tl(hd(y0))))))) -> c16(MARK(incr(adx(tl(tl(hd(y0))))))) MARK(hd(incr(adx(tl(tl(tl(y0))))))) -> c16(MARK(incr(adx(tl(tl(tl(y0))))))) MARK(hd(incr(adx(tl(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(tl(cons(y0, y1))))))) MARK(hd(incr(adx(tl(tl(y0)))))) -> c16(MARK(incr(adx(tl(tl(y0)))))) MARK(hd(incr(adx(tl(nats))))) -> c16(MARK(incr(adx(tl(nats))))) MARK(hd(incr(adx(hd(adx(0)))))) -> c16(MARK(incr(adx(hd(adx(0)))))) MARK(hd(incr(adx(hd(adx(s(y0))))))) -> c16(MARK(incr(adx(hd(adx(s(y0))))))) MARK(hd(incr(adx(hd(incr(0)))))) -> c16(MARK(incr(adx(hd(incr(0)))))) MARK(hd(incr(adx(hd(incr(s(y0))))))) -> c16(MARK(incr(adx(hd(incr(s(y0))))))) MARK(hd(incr(adx(hd(hd(zeros)))))) -> c16(MARK(incr(adx(hd(hd(zeros)))))) MARK(hd(incr(adx(tl(hd(zeros)))))) -> c16(MARK(incr(adx(tl(hd(zeros)))))) MARK(hd(incr(adx(tl(adx(0)))))) -> c16(MARK(incr(adx(tl(adx(0)))))) MARK(hd(incr(adx(hd(tl(zeros)))))) -> c16(MARK(incr(adx(hd(tl(zeros)))))) MARK(hd(incr(adx(tl(tl(zeros)))))) -> c16(MARK(incr(adx(tl(tl(zeros)))))) MARK(hd(incr(adx(tl(adx(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) MARK(hd(incr(adx(tl(incr(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) MARK(hd(incr(hd(adx(nats))))) -> c16(MARK(incr(hd(adx(nats))))) MARK(hd(incr(hd(adx(zeros))))) -> c16(MARK(incr(hd(adx(zeros))))) MARK(hd(incr(hd(adx(cons(y0, y1)))))) -> c16(MARK(incr(hd(adx(cons(y0, y1)))))) MARK(hd(incr(tl(adx(nats))))) -> c16(MARK(incr(tl(adx(nats))))) MARK(hd(incr(tl(adx(zeros))))) -> c16(MARK(incr(tl(adx(zeros))))) MARK(hd(incr(tl(adx(cons(y0, y1)))))) -> c16(MARK(incr(tl(adx(cons(y0, y1)))))) MARK(hd(incr(tl(incr(s(y0)))))) -> c16(MARK(incr(tl(incr(s(y0)))))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c16_2, c16_1, c17_2, c17_1, c8_1, c10_1, c13_1, c15_1 ---------------------------------------- (209) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(hd(incr(x0))) -> c16(MARK(incr(x0))) by MARK(hd(incr(incr(y0)))) -> c16(MARK(incr(incr(y0)))) MARK(hd(incr(hd(cons(y0, y1))))) -> c16(MARK(incr(hd(cons(y0, y1))))) MARK(hd(incr(tl(cons(y0, y1))))) -> c16(MARK(incr(tl(cons(y0, y1))))) MARK(hd(incr(hd(adx(adx(y0)))))) -> c16(MARK(incr(hd(adx(adx(y0)))))) MARK(hd(incr(hd(adx(incr(y0)))))) -> c16(MARK(incr(hd(adx(incr(y0)))))) MARK(hd(incr(hd(adx(hd(y0)))))) -> c16(MARK(incr(hd(adx(hd(y0)))))) MARK(hd(incr(hd(adx(tl(y0)))))) -> c16(MARK(incr(hd(adx(tl(y0)))))) MARK(hd(incr(hd(adx(y0))))) -> c16(MARK(incr(hd(adx(y0))))) MARK(hd(incr(hd(incr(nats))))) -> c16(MARK(incr(hd(incr(nats))))) MARK(hd(incr(hd(incr(adx(y0)))))) -> c16(MARK(incr(hd(incr(adx(y0)))))) MARK(hd(incr(hd(incr(zeros))))) -> c16(MARK(incr(hd(incr(zeros))))) MARK(hd(incr(hd(incr(incr(y0)))))) -> c16(MARK(incr(hd(incr(incr(y0)))))) MARK(hd(incr(hd(incr(hd(y0)))))) -> c16(MARK(incr(hd(incr(hd(y0)))))) MARK(hd(incr(hd(incr(tl(y0)))))) -> c16(MARK(incr(hd(incr(tl(y0)))))) MARK(hd(incr(hd(incr(cons(y0, y1)))))) -> c16(MARK(incr(hd(incr(cons(y0, y1)))))) MARK(hd(incr(hd(incr(y0))))) -> c16(MARK(incr(hd(incr(y0))))) MARK(hd(incr(hd(hd(nats))))) -> c16(MARK(incr(hd(hd(nats))))) MARK(hd(incr(hd(hd(adx(y0)))))) -> c16(MARK(incr(hd(hd(adx(y0)))))) MARK(hd(incr(hd(hd(incr(y0)))))) -> c16(MARK(incr(hd(hd(incr(y0)))))) MARK(hd(incr(hd(hd(hd(y0)))))) -> c16(MARK(incr(hd(hd(hd(y0)))))) MARK(hd(incr(hd(hd(tl(y0)))))) -> c16(MARK(incr(hd(hd(tl(y0)))))) MARK(hd(incr(hd(hd(cons(y0, y1)))))) -> c16(MARK(incr(hd(hd(cons(y0, y1)))))) MARK(hd(incr(hd(hd(y0))))) -> c16(MARK(incr(hd(hd(y0))))) MARK(hd(incr(hd(tl(nats))))) -> c16(MARK(incr(hd(tl(nats))))) MARK(hd(incr(hd(tl(adx(y0)))))) -> c16(MARK(incr(hd(tl(adx(y0)))))) MARK(hd(incr(hd(tl(incr(y0)))))) -> c16(MARK(incr(hd(tl(incr(y0)))))) MARK(hd(incr(hd(tl(hd(y0)))))) -> c16(MARK(incr(hd(tl(hd(y0)))))) MARK(hd(incr(hd(tl(tl(y0)))))) -> c16(MARK(incr(hd(tl(tl(y0)))))) MARK(hd(incr(hd(tl(cons(y0, y1)))))) -> c16(MARK(incr(hd(tl(cons(y0, y1)))))) MARK(hd(incr(hd(tl(y0))))) -> c16(MARK(incr(hd(tl(y0))))) MARK(hd(incr(hd(nats)))) -> c16(MARK(incr(hd(nats)))) MARK(hd(incr(tl(adx(adx(y0)))))) -> c16(MARK(incr(tl(adx(adx(y0)))))) MARK(hd(incr(tl(adx(incr(y0)))))) -> c16(MARK(incr(tl(adx(incr(y0)))))) MARK(hd(incr(tl(adx(hd(y0)))))) -> c16(MARK(incr(tl(adx(hd(y0)))))) MARK(hd(incr(tl(adx(tl(y0)))))) -> c16(MARK(incr(tl(adx(tl(y0)))))) MARK(hd(incr(tl(adx(y0))))) -> c16(MARK(incr(tl(adx(y0))))) MARK(hd(incr(tl(incr(nats))))) -> c16(MARK(incr(tl(incr(nats))))) MARK(hd(incr(tl(incr(adx(y0)))))) -> c16(MARK(incr(tl(incr(adx(y0)))))) MARK(hd(incr(tl(incr(zeros))))) -> c16(MARK(incr(tl(incr(zeros))))) MARK(hd(incr(tl(incr(incr(y0)))))) -> c16(MARK(incr(tl(incr(incr(y0)))))) MARK(hd(incr(tl(incr(hd(y0)))))) -> c16(MARK(incr(tl(incr(hd(y0)))))) MARK(hd(incr(tl(incr(tl(y0)))))) -> c16(MARK(incr(tl(incr(tl(y0)))))) MARK(hd(incr(tl(incr(cons(y0, y1)))))) -> c16(MARK(incr(tl(incr(cons(y0, y1)))))) MARK(hd(incr(tl(incr(y0))))) -> c16(MARK(incr(tl(incr(y0))))) MARK(hd(incr(tl(hd(nats))))) -> c16(MARK(incr(tl(hd(nats))))) MARK(hd(incr(tl(hd(adx(y0)))))) -> c16(MARK(incr(tl(hd(adx(y0)))))) MARK(hd(incr(tl(hd(incr(y0)))))) -> c16(MARK(incr(tl(hd(incr(y0)))))) MARK(hd(incr(tl(hd(hd(y0)))))) -> c16(MARK(incr(tl(hd(hd(y0)))))) MARK(hd(incr(tl(hd(tl(y0)))))) -> c16(MARK(incr(tl(hd(tl(y0)))))) MARK(hd(incr(tl(hd(cons(y0, y1)))))) -> c16(MARK(incr(tl(hd(cons(y0, y1)))))) MARK(hd(incr(tl(hd(y0))))) -> c16(MARK(incr(tl(hd(y0))))) MARK(hd(incr(tl(tl(nats))))) -> c16(MARK(incr(tl(tl(nats))))) MARK(hd(incr(tl(tl(adx(y0)))))) -> c16(MARK(incr(tl(tl(adx(y0)))))) MARK(hd(incr(tl(tl(incr(y0)))))) -> c16(MARK(incr(tl(tl(incr(y0)))))) MARK(hd(incr(tl(tl(hd(y0)))))) -> c16(MARK(incr(tl(tl(hd(y0)))))) MARK(hd(incr(tl(tl(tl(y0)))))) -> c16(MARK(incr(tl(tl(tl(y0)))))) MARK(hd(incr(tl(tl(cons(y0, y1)))))) -> c16(MARK(incr(tl(tl(cons(y0, y1)))))) MARK(hd(incr(tl(tl(y0))))) -> c16(MARK(incr(tl(tl(y0))))) MARK(hd(incr(tl(nats)))) -> c16(MARK(incr(tl(nats)))) MARK(hd(incr(hd(incr(0))))) -> c16(MARK(incr(hd(incr(0))))) MARK(hd(incr(hd(incr(s(y0)))))) -> c16(MARK(incr(hd(incr(s(y0)))))) MARK(hd(incr(hd(hd(zeros))))) -> c16(MARK(incr(hd(hd(zeros))))) MARK(hd(incr(tl(hd(zeros))))) -> c16(MARK(incr(tl(hd(zeros))))) MARK(hd(incr(hd(tl(zeros))))) -> c16(MARK(incr(hd(tl(zeros))))) MARK(hd(incr(tl(tl(zeros))))) -> c16(MARK(incr(tl(tl(zeros))))) MARK(hd(incr(tl(incr(0))))) -> c16(MARK(incr(tl(incr(0))))) MARK(hd(incr(adx(adx(y0))))) -> c16(MARK(incr(adx(adx(y0))))) MARK(hd(incr(adx(incr(y0))))) -> c16(MARK(incr(adx(incr(y0))))) MARK(hd(incr(adx(hd(cons(y0, y1)))))) -> c16(MARK(incr(adx(hd(cons(y0, y1)))))) MARK(hd(incr(adx(tl(cons(y0, y1)))))) -> c16(MARK(incr(adx(tl(cons(y0, y1)))))) MARK(hd(incr(adx(hd(adx(nats)))))) -> c16(MARK(incr(adx(hd(adx(nats)))))) MARK(hd(incr(adx(hd(adx(adx(y0))))))) -> c16(MARK(incr(adx(hd(adx(adx(y0))))))) MARK(hd(incr(adx(hd(adx(zeros)))))) -> c16(MARK(incr(adx(hd(adx(zeros)))))) MARK(hd(incr(adx(hd(adx(incr(y0))))))) -> c16(MARK(incr(adx(hd(adx(incr(y0))))))) MARK(hd(incr(adx(hd(adx(hd(y0))))))) -> c16(MARK(incr(adx(hd(adx(hd(y0))))))) MARK(hd(incr(adx(hd(adx(tl(y0))))))) -> c16(MARK(incr(adx(hd(adx(tl(y0))))))) MARK(hd(incr(adx(hd(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(adx(cons(y0, y1))))))) MARK(hd(incr(adx(hd(adx(y0)))))) -> c16(MARK(incr(adx(hd(adx(y0)))))) MARK(hd(incr(adx(hd(incr(nats)))))) -> c16(MARK(incr(adx(hd(incr(nats)))))) MARK(hd(incr(adx(hd(incr(adx(y0))))))) -> c16(MARK(incr(adx(hd(incr(adx(y0))))))) MARK(hd(incr(adx(hd(incr(zeros)))))) -> c16(MARK(incr(adx(hd(incr(zeros)))))) MARK(hd(incr(adx(hd(incr(incr(y0))))))) -> c16(MARK(incr(adx(hd(incr(incr(y0))))))) MARK(hd(incr(adx(hd(incr(hd(y0))))))) -> c16(MARK(incr(adx(hd(incr(hd(y0))))))) MARK(hd(incr(adx(hd(incr(tl(y0))))))) -> c16(MARK(incr(adx(hd(incr(tl(y0))))))) MARK(hd(incr(adx(hd(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(incr(cons(y0, y1))))))) MARK(hd(incr(adx(hd(incr(y0)))))) -> c16(MARK(incr(adx(hd(incr(y0)))))) MARK(hd(incr(adx(hd(hd(nats)))))) -> c16(MARK(incr(adx(hd(hd(nats)))))) MARK(hd(incr(adx(hd(hd(adx(y0))))))) -> c16(MARK(incr(adx(hd(hd(adx(y0))))))) MARK(hd(incr(adx(hd(hd(incr(y0))))))) -> c16(MARK(incr(adx(hd(hd(incr(y0))))))) MARK(hd(incr(adx(hd(hd(hd(y0))))))) -> c16(MARK(incr(adx(hd(hd(hd(y0))))))) MARK(hd(incr(adx(hd(hd(tl(y0))))))) -> c16(MARK(incr(adx(hd(hd(tl(y0))))))) MARK(hd(incr(adx(hd(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(hd(cons(y0, y1))))))) MARK(hd(incr(adx(hd(hd(y0)))))) -> c16(MARK(incr(adx(hd(hd(y0)))))) MARK(hd(incr(adx(hd(tl(nats)))))) -> c16(MARK(incr(adx(hd(tl(nats)))))) MARK(hd(incr(adx(hd(tl(adx(y0))))))) -> c16(MARK(incr(adx(hd(tl(adx(y0))))))) MARK(hd(incr(adx(hd(tl(incr(y0))))))) -> c16(MARK(incr(adx(hd(tl(incr(y0))))))) MARK(hd(incr(adx(hd(tl(hd(y0))))))) -> c16(MARK(incr(adx(hd(tl(hd(y0))))))) MARK(hd(incr(adx(hd(tl(tl(y0))))))) -> c16(MARK(incr(adx(hd(tl(tl(y0))))))) MARK(hd(incr(adx(hd(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(tl(cons(y0, y1))))))) MARK(hd(incr(adx(hd(tl(y0)))))) -> c16(MARK(incr(adx(hd(tl(y0)))))) MARK(hd(incr(adx(hd(nats))))) -> c16(MARK(incr(adx(hd(nats))))) MARK(hd(incr(adx(tl(adx(nats)))))) -> c16(MARK(incr(adx(tl(adx(nats)))))) MARK(hd(incr(adx(tl(adx(adx(y0))))))) -> c16(MARK(incr(adx(tl(adx(adx(y0))))))) MARK(hd(incr(adx(tl(adx(zeros)))))) -> c16(MARK(incr(adx(tl(adx(zeros)))))) MARK(hd(incr(adx(tl(adx(incr(y0))))))) -> c16(MARK(incr(adx(tl(adx(incr(y0))))))) MARK(hd(incr(adx(tl(adx(hd(y0))))))) -> c16(MARK(incr(adx(tl(adx(hd(y0))))))) MARK(hd(incr(adx(tl(adx(tl(y0))))))) -> c16(MARK(incr(adx(tl(adx(tl(y0))))))) MARK(hd(incr(adx(tl(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(adx(cons(y0, y1))))))) MARK(hd(incr(adx(tl(adx(y0)))))) -> c16(MARK(incr(adx(tl(adx(y0)))))) MARK(hd(incr(adx(tl(incr(nats)))))) -> c16(MARK(incr(adx(tl(incr(nats)))))) MARK(hd(incr(adx(tl(incr(adx(y0))))))) -> c16(MARK(incr(adx(tl(incr(adx(y0))))))) MARK(hd(incr(adx(tl(incr(zeros)))))) -> c16(MARK(incr(adx(tl(incr(zeros)))))) MARK(hd(incr(adx(tl(incr(incr(y0))))))) -> c16(MARK(incr(adx(tl(incr(incr(y0))))))) MARK(hd(incr(adx(tl(incr(hd(y0))))))) -> c16(MARK(incr(adx(tl(incr(hd(y0))))))) MARK(hd(incr(adx(tl(incr(tl(y0))))))) -> c16(MARK(incr(adx(tl(incr(tl(y0))))))) MARK(hd(incr(adx(tl(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(incr(cons(y0, y1))))))) MARK(hd(incr(adx(tl(incr(s(y0))))))) -> c16(MARK(incr(adx(tl(incr(s(y0))))))) MARK(hd(incr(adx(tl(incr(y0)))))) -> c16(MARK(incr(adx(tl(incr(y0)))))) MARK(hd(incr(adx(tl(hd(nats)))))) -> c16(MARK(incr(adx(tl(hd(nats)))))) MARK(hd(incr(adx(tl(hd(adx(y0))))))) -> c16(MARK(incr(adx(tl(hd(adx(y0))))))) MARK(hd(incr(adx(tl(hd(incr(y0))))))) -> c16(MARK(incr(adx(tl(hd(incr(y0))))))) MARK(hd(incr(adx(tl(hd(hd(y0))))))) -> c16(MARK(incr(adx(tl(hd(hd(y0))))))) MARK(hd(incr(adx(tl(hd(tl(y0))))))) -> c16(MARK(incr(adx(tl(hd(tl(y0))))))) MARK(hd(incr(adx(tl(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(hd(cons(y0, y1))))))) MARK(hd(incr(adx(tl(hd(y0)))))) -> c16(MARK(incr(adx(tl(hd(y0)))))) MARK(hd(incr(adx(tl(tl(nats)))))) -> c16(MARK(incr(adx(tl(tl(nats)))))) MARK(hd(incr(adx(tl(tl(adx(y0))))))) -> c16(MARK(incr(adx(tl(tl(adx(y0))))))) MARK(hd(incr(adx(tl(tl(incr(y0))))))) -> c16(MARK(incr(adx(tl(tl(incr(y0))))))) MARK(hd(incr(adx(tl(tl(hd(y0))))))) -> c16(MARK(incr(adx(tl(tl(hd(y0))))))) MARK(hd(incr(adx(tl(tl(tl(y0))))))) -> c16(MARK(incr(adx(tl(tl(tl(y0))))))) MARK(hd(incr(adx(tl(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(tl(cons(y0, y1))))))) MARK(hd(incr(adx(tl(tl(y0)))))) -> c16(MARK(incr(adx(tl(tl(y0)))))) MARK(hd(incr(adx(tl(nats))))) -> c16(MARK(incr(adx(tl(nats))))) MARK(hd(incr(adx(hd(adx(0)))))) -> c16(MARK(incr(adx(hd(adx(0)))))) MARK(hd(incr(adx(hd(adx(s(y0))))))) -> c16(MARK(incr(adx(hd(adx(s(y0))))))) MARK(hd(incr(adx(hd(incr(0)))))) -> c16(MARK(incr(adx(hd(incr(0)))))) MARK(hd(incr(adx(hd(incr(s(y0))))))) -> c16(MARK(incr(adx(hd(incr(s(y0))))))) MARK(hd(incr(adx(hd(hd(zeros)))))) -> c16(MARK(incr(adx(hd(hd(zeros)))))) MARK(hd(incr(adx(tl(hd(zeros)))))) -> c16(MARK(incr(adx(tl(hd(zeros)))))) MARK(hd(incr(adx(tl(adx(0)))))) -> c16(MARK(incr(adx(tl(adx(0)))))) MARK(hd(incr(adx(hd(tl(zeros)))))) -> c16(MARK(incr(adx(hd(tl(zeros)))))) MARK(hd(incr(adx(tl(tl(zeros)))))) -> c16(MARK(incr(adx(tl(tl(zeros)))))) MARK(hd(incr(adx(tl(adx(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) MARK(hd(incr(adx(tl(incr(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) MARK(hd(incr(hd(adx(nats))))) -> c16(MARK(incr(hd(adx(nats))))) MARK(hd(incr(hd(adx(zeros))))) -> c16(MARK(incr(hd(adx(zeros))))) MARK(hd(incr(hd(adx(cons(y0, y1)))))) -> c16(MARK(incr(hd(adx(cons(y0, y1)))))) MARK(hd(incr(tl(adx(nats))))) -> c16(MARK(incr(tl(adx(nats))))) MARK(hd(incr(tl(adx(zeros))))) -> c16(MARK(incr(tl(adx(zeros))))) MARK(hd(incr(tl(adx(cons(y0, y1)))))) -> c16(MARK(incr(tl(adx(cons(y0, y1)))))) MARK(hd(incr(tl(incr(s(y0)))))) -> c16(MARK(incr(tl(incr(s(y0)))))) ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) MARK(tl(cons(z0, adx(y1)))) -> c17(A__TL(cons(z0, adx(y1)))) MARK(tl(cons(z0, incr(y1)))) -> c17(A__TL(cons(z0, incr(y1)))) MARK(tl(cons(z0, hd(cons(y1, y2))))) -> c17(A__TL(cons(z0, hd(cons(y1, y2))))) MARK(tl(cons(z0, tl(cons(y1, y2))))) -> c17(A__TL(cons(z0, tl(cons(y1, y2))))) MARK(tl(cons(z0, hd(adx(nats))))) -> c17(A__TL(cons(z0, hd(adx(nats))))) MARK(tl(cons(z0, hd(adx(adx(y1)))))) -> c17(A__TL(cons(z0, hd(adx(adx(y1)))))) MARK(tl(cons(z0, hd(adx(zeros))))) -> c17(A__TL(cons(z0, hd(adx(zeros))))) MARK(tl(cons(z0, hd(adx(incr(y1)))))) -> c17(A__TL(cons(z0, hd(adx(incr(y1)))))) MARK(tl(cons(z0, hd(adx(hd(y1)))))) -> c17(A__TL(cons(z0, hd(adx(hd(y1)))))) MARK(tl(cons(z0, hd(adx(tl(y1)))))) -> c17(A__TL(cons(z0, hd(adx(tl(y1)))))) MARK(tl(cons(z0, hd(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(adx(cons(y1, y2)))))) MARK(tl(cons(z0, hd(adx(y1))))) -> c17(A__TL(cons(z0, hd(adx(y1))))) MARK(tl(cons(z0, hd(incr(nats))))) -> c17(A__TL(cons(z0, hd(incr(nats))))) MARK(tl(cons(z0, hd(incr(adx(y1)))))) -> c17(A__TL(cons(z0, hd(incr(adx(y1)))))) MARK(tl(cons(z0, hd(incr(zeros))))) -> c17(A__TL(cons(z0, hd(incr(zeros))))) MARK(tl(cons(z0, hd(incr(incr(y1)))))) -> c17(A__TL(cons(z0, hd(incr(incr(y1)))))) MARK(tl(cons(z0, hd(incr(hd(y1)))))) -> c17(A__TL(cons(z0, hd(incr(hd(y1)))))) MARK(tl(cons(z0, hd(incr(tl(y1)))))) -> c17(A__TL(cons(z0, hd(incr(tl(y1)))))) MARK(tl(cons(z0, hd(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(incr(cons(y1, y2)))))) MARK(tl(cons(z0, hd(incr(y1))))) -> c17(A__TL(cons(z0, hd(incr(y1))))) MARK(tl(cons(z0, hd(hd(nats))))) -> c17(A__TL(cons(z0, hd(hd(nats))))) MARK(tl(cons(z0, hd(hd(adx(y1)))))) -> c17(A__TL(cons(z0, hd(hd(adx(y1)))))) MARK(tl(cons(z0, hd(hd(incr(y1)))))) -> c17(A__TL(cons(z0, hd(hd(incr(y1)))))) MARK(tl(cons(z0, hd(hd(hd(y1)))))) -> c17(A__TL(cons(z0, hd(hd(hd(y1)))))) MARK(tl(cons(z0, hd(hd(tl(y1)))))) -> c17(A__TL(cons(z0, hd(hd(tl(y1)))))) MARK(tl(cons(z0, hd(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(hd(cons(y1, y2)))))) MARK(tl(cons(z0, hd(hd(y1))))) -> c17(A__TL(cons(z0, hd(hd(y1))))) MARK(tl(cons(z0, hd(tl(nats))))) -> c17(A__TL(cons(z0, hd(tl(nats))))) MARK(tl(cons(z0, hd(tl(adx(y1)))))) -> c17(A__TL(cons(z0, hd(tl(adx(y1)))))) MARK(tl(cons(z0, hd(tl(zeros))))) -> c17(A__TL(cons(z0, hd(tl(zeros))))) MARK(tl(cons(z0, hd(tl(incr(y1)))))) -> c17(A__TL(cons(z0, hd(tl(incr(y1)))))) MARK(tl(cons(z0, hd(tl(hd(y1)))))) -> c17(A__TL(cons(z0, hd(tl(hd(y1)))))) MARK(tl(cons(z0, hd(tl(tl(y1)))))) -> c17(A__TL(cons(z0, hd(tl(tl(y1)))))) MARK(tl(cons(z0, hd(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(tl(cons(y1, y2)))))) MARK(tl(cons(z0, hd(tl(y1))))) -> c17(A__TL(cons(z0, hd(tl(y1))))) MARK(tl(cons(z0, hd(nats)))) -> c17(A__TL(cons(z0, hd(nats)))) MARK(tl(cons(z0, tl(adx(nats))))) -> c17(A__TL(cons(z0, tl(adx(nats))))) MARK(tl(cons(z0, tl(adx(adx(y1)))))) -> c17(A__TL(cons(z0, tl(adx(adx(y1)))))) MARK(tl(cons(z0, tl(adx(zeros))))) -> c17(A__TL(cons(z0, tl(adx(zeros))))) MARK(tl(cons(z0, tl(adx(incr(y1)))))) -> c17(A__TL(cons(z0, tl(adx(incr(y1)))))) MARK(tl(cons(z0, tl(adx(hd(y1)))))) -> c17(A__TL(cons(z0, tl(adx(hd(y1)))))) MARK(tl(cons(z0, tl(adx(tl(y1)))))) -> c17(A__TL(cons(z0, tl(adx(tl(y1)))))) MARK(tl(cons(z0, tl(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(adx(cons(y1, y2)))))) MARK(tl(cons(z0, tl(adx(s(y1)))))) -> c17(A__TL(cons(z0, tl(adx(s(y1)))))) MARK(tl(cons(z0, tl(adx(y1))))) -> c17(A__TL(cons(z0, tl(adx(y1))))) MARK(tl(cons(z0, tl(incr(nats))))) -> c17(A__TL(cons(z0, tl(incr(nats))))) MARK(tl(cons(z0, tl(incr(adx(y1)))))) -> c17(A__TL(cons(z0, tl(incr(adx(y1)))))) MARK(tl(cons(z0, tl(incr(zeros))))) -> c17(A__TL(cons(z0, tl(incr(zeros))))) MARK(tl(cons(z0, tl(incr(incr(y1)))))) -> c17(A__TL(cons(z0, tl(incr(incr(y1)))))) MARK(tl(cons(z0, tl(incr(hd(y1)))))) -> c17(A__TL(cons(z0, tl(incr(hd(y1)))))) MARK(tl(cons(z0, tl(incr(tl(y1)))))) -> c17(A__TL(cons(z0, tl(incr(tl(y1)))))) MARK(tl(cons(z0, tl(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(incr(cons(y1, y2)))))) MARK(tl(cons(z0, tl(incr(0))))) -> c17(A__TL(cons(z0, tl(incr(0))))) MARK(tl(cons(z0, tl(incr(s(y1)))))) -> c17(A__TL(cons(z0, tl(incr(s(y1)))))) MARK(tl(cons(z0, tl(incr(y1))))) -> c17(A__TL(cons(z0, tl(incr(y1))))) MARK(tl(cons(z0, tl(hd(nats))))) -> c17(A__TL(cons(z0, tl(hd(nats))))) MARK(tl(cons(z0, tl(hd(adx(y1)))))) -> c17(A__TL(cons(z0, tl(hd(adx(y1)))))) MARK(tl(cons(z0, tl(hd(incr(y1)))))) -> c17(A__TL(cons(z0, tl(hd(incr(y1)))))) MARK(tl(cons(z0, tl(hd(hd(y1)))))) -> c17(A__TL(cons(z0, tl(hd(hd(y1)))))) MARK(tl(cons(z0, tl(hd(tl(y1)))))) -> c17(A__TL(cons(z0, tl(hd(tl(y1)))))) MARK(tl(cons(z0, tl(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(hd(cons(y1, y2)))))) MARK(tl(cons(z0, tl(hd(y1))))) -> c17(A__TL(cons(z0, tl(hd(y1))))) MARK(tl(cons(z0, tl(tl(nats))))) -> c17(A__TL(cons(z0, tl(tl(nats))))) MARK(tl(cons(z0, tl(tl(adx(y1)))))) -> c17(A__TL(cons(z0, tl(tl(adx(y1)))))) MARK(tl(cons(z0, tl(tl(zeros))))) -> c17(A__TL(cons(z0, tl(tl(zeros))))) MARK(tl(cons(z0, tl(tl(incr(y1)))))) -> c17(A__TL(cons(z0, tl(tl(incr(y1)))))) MARK(tl(cons(z0, tl(tl(hd(y1)))))) -> c17(A__TL(cons(z0, tl(tl(hd(y1)))))) MARK(tl(cons(z0, tl(tl(tl(y1)))))) -> c17(A__TL(cons(z0, tl(tl(tl(y1)))))) MARK(tl(cons(z0, tl(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(tl(cons(y1, y2)))))) MARK(tl(cons(z0, tl(tl(y1))))) -> c17(A__TL(cons(z0, tl(tl(y1))))) MARK(tl(cons(z0, tl(nats)))) -> c17(A__TL(cons(z0, tl(nats)))) MARK(tl(cons(z0, hd(adx(0))))) -> c17(A__TL(cons(z0, hd(adx(0))))) MARK(tl(cons(z0, hd(adx(s(y1)))))) -> c17(A__TL(cons(z0, hd(adx(s(y1)))))) MARK(tl(cons(z0, hd(incr(0))))) -> c17(A__TL(cons(z0, hd(incr(0))))) MARK(tl(cons(z0, hd(incr(s(y1)))))) -> c17(A__TL(cons(z0, hd(incr(s(y1)))))) MARK(tl(cons(z0, hd(hd(zeros))))) -> c17(A__TL(cons(z0, hd(hd(zeros))))) MARK(tl(cons(z0, tl(hd(zeros))))) -> c17(A__TL(cons(z0, tl(hd(zeros))))) MARK(tl(cons(z0, tl(adx(0))))) -> c17(A__TL(cons(z0, tl(adx(0))))) MARK(hd(adx(adx(y0)))) -> c16(MARK(adx(adx(y0)))) MARK(hd(adx(incr(y0)))) -> c16(MARK(adx(incr(y0)))) MARK(hd(adx(hd(cons(y0, y1))))) -> c16(MARK(adx(hd(cons(y0, y1))))) MARK(hd(adx(tl(cons(y0, y1))))) -> c16(MARK(adx(tl(cons(y0, y1))))) MARK(hd(adx(hd(adx(nats))))) -> c16(MARK(adx(hd(adx(nats))))) MARK(hd(adx(hd(adx(adx(y0)))))) -> c16(MARK(adx(hd(adx(adx(y0)))))) MARK(hd(adx(hd(adx(zeros))))) -> c16(MARK(adx(hd(adx(zeros))))) MARK(hd(adx(hd(adx(incr(y0)))))) -> c16(MARK(adx(hd(adx(incr(y0)))))) MARK(hd(adx(hd(adx(hd(y0)))))) -> c16(MARK(adx(hd(adx(hd(y0)))))) MARK(hd(adx(hd(adx(tl(y0)))))) -> c16(MARK(adx(hd(adx(tl(y0)))))) MARK(hd(adx(hd(adx(cons(y0, y1)))))) -> c16(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(hd(adx(hd(adx(y0))))) -> c16(MARK(adx(hd(adx(y0))))) MARK(hd(adx(hd(incr(nats))))) -> c16(MARK(adx(hd(incr(nats))))) MARK(hd(adx(hd(incr(adx(y0)))))) -> c16(MARK(adx(hd(incr(adx(y0)))))) MARK(hd(adx(hd(incr(zeros))))) -> c16(MARK(adx(hd(incr(zeros))))) MARK(hd(adx(hd(incr(incr(y0)))))) -> c16(MARK(adx(hd(incr(incr(y0)))))) MARK(hd(adx(hd(incr(hd(y0)))))) -> c16(MARK(adx(hd(incr(hd(y0)))))) MARK(hd(adx(hd(incr(tl(y0)))))) -> c16(MARK(adx(hd(incr(tl(y0)))))) MARK(hd(adx(hd(incr(cons(y0, y1)))))) -> c16(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(hd(adx(hd(incr(y0))))) -> c16(MARK(adx(hd(incr(y0))))) MARK(hd(adx(hd(hd(nats))))) -> c16(MARK(adx(hd(hd(nats))))) MARK(hd(adx(hd(hd(adx(y0)))))) -> c16(MARK(adx(hd(hd(adx(y0)))))) MARK(hd(adx(hd(hd(incr(y0)))))) -> c16(MARK(adx(hd(hd(incr(y0)))))) MARK(hd(adx(hd(hd(hd(y0)))))) -> c16(MARK(adx(hd(hd(hd(y0)))))) MARK(hd(adx(hd(hd(tl(y0)))))) -> c16(MARK(adx(hd(hd(tl(y0)))))) MARK(hd(adx(hd(hd(cons(y0, y1)))))) -> c16(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(hd(adx(hd(hd(y0))))) -> c16(MARK(adx(hd(hd(y0))))) MARK(hd(adx(hd(tl(nats))))) -> c16(MARK(adx(hd(tl(nats))))) MARK(hd(adx(hd(tl(adx(y0)))))) -> c16(MARK(adx(hd(tl(adx(y0)))))) MARK(hd(adx(hd(tl(incr(y0)))))) -> c16(MARK(adx(hd(tl(incr(y0)))))) MARK(hd(adx(hd(tl(hd(y0)))))) -> c16(MARK(adx(hd(tl(hd(y0)))))) MARK(hd(adx(hd(tl(tl(y0)))))) -> c16(MARK(adx(hd(tl(tl(y0)))))) MARK(hd(adx(hd(tl(cons(y0, y1)))))) -> c16(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(hd(adx(hd(tl(y0))))) -> c16(MARK(adx(hd(tl(y0))))) MARK(hd(adx(hd(nats)))) -> c16(MARK(adx(hd(nats)))) MARK(hd(adx(tl(adx(nats))))) -> c16(MARK(adx(tl(adx(nats))))) MARK(hd(adx(tl(adx(adx(y0)))))) -> c16(MARK(adx(tl(adx(adx(y0)))))) MARK(hd(adx(tl(adx(zeros))))) -> c16(MARK(adx(tl(adx(zeros))))) MARK(hd(adx(tl(adx(incr(y0)))))) -> c16(MARK(adx(tl(adx(incr(y0)))))) MARK(hd(adx(tl(adx(hd(y0)))))) -> c16(MARK(adx(tl(adx(hd(y0)))))) MARK(hd(adx(tl(adx(tl(y0)))))) -> c16(MARK(adx(tl(adx(tl(y0)))))) MARK(hd(adx(tl(adx(cons(y0, y1)))))) -> c16(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(hd(adx(tl(adx(y0))))) -> c16(MARK(adx(tl(adx(y0))))) MARK(hd(adx(tl(incr(nats))))) -> c16(MARK(adx(tl(incr(nats))))) MARK(hd(adx(tl(incr(adx(y0)))))) -> c16(MARK(adx(tl(incr(adx(y0)))))) MARK(hd(adx(tl(incr(zeros))))) -> c16(MARK(adx(tl(incr(zeros))))) MARK(hd(adx(tl(incr(incr(y0)))))) -> c16(MARK(adx(tl(incr(incr(y0)))))) MARK(hd(adx(tl(incr(hd(y0)))))) -> c16(MARK(adx(tl(incr(hd(y0)))))) MARK(hd(adx(tl(incr(tl(y0)))))) -> c16(MARK(adx(tl(incr(tl(y0)))))) MARK(hd(adx(tl(incr(cons(y0, y1)))))) -> c16(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(hd(adx(tl(incr(s(y0)))))) -> c16(MARK(adx(tl(incr(s(y0)))))) MARK(hd(adx(tl(incr(y0))))) -> c16(MARK(adx(tl(incr(y0))))) MARK(hd(adx(tl(hd(nats))))) -> c16(MARK(adx(tl(hd(nats))))) MARK(hd(adx(tl(hd(adx(y0)))))) -> c16(MARK(adx(tl(hd(adx(y0)))))) MARK(hd(adx(tl(hd(incr(y0)))))) -> c16(MARK(adx(tl(hd(incr(y0)))))) MARK(hd(adx(tl(hd(hd(y0)))))) -> c16(MARK(adx(tl(hd(hd(y0)))))) MARK(hd(adx(tl(hd(tl(y0)))))) -> c16(MARK(adx(tl(hd(tl(y0)))))) MARK(hd(adx(tl(hd(cons(y0, y1)))))) -> c16(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(hd(adx(tl(hd(y0))))) -> c16(MARK(adx(tl(hd(y0))))) MARK(hd(adx(tl(tl(nats))))) -> c16(MARK(adx(tl(tl(nats))))) MARK(hd(adx(tl(tl(adx(y0)))))) -> c16(MARK(adx(tl(tl(adx(y0)))))) MARK(hd(adx(tl(tl(incr(y0)))))) -> c16(MARK(adx(tl(tl(incr(y0)))))) MARK(hd(adx(tl(tl(hd(y0)))))) -> c16(MARK(adx(tl(tl(hd(y0)))))) MARK(hd(adx(tl(tl(tl(y0)))))) -> c16(MARK(adx(tl(tl(tl(y0)))))) MARK(hd(adx(tl(tl(cons(y0, y1)))))) -> c16(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(hd(adx(tl(tl(y0))))) -> c16(MARK(adx(tl(tl(y0))))) MARK(hd(adx(tl(nats)))) -> c16(MARK(adx(tl(nats)))) MARK(hd(adx(hd(adx(0))))) -> c16(MARK(adx(hd(adx(0))))) MARK(hd(adx(hd(adx(s(y0)))))) -> c16(MARK(adx(hd(adx(s(y0)))))) MARK(hd(adx(hd(incr(0))))) -> c16(MARK(adx(hd(incr(0))))) MARK(hd(adx(hd(incr(s(y0)))))) -> c16(MARK(adx(hd(incr(s(y0)))))) MARK(hd(adx(hd(hd(zeros))))) -> c16(MARK(adx(hd(hd(zeros))))) MARK(hd(adx(tl(hd(zeros))))) -> c16(MARK(adx(tl(hd(zeros))))) MARK(hd(adx(tl(adx(0))))) -> c16(MARK(adx(tl(adx(0))))) MARK(hd(adx(hd(tl(zeros))))) -> c16(MARK(adx(hd(tl(zeros))))) MARK(hd(adx(tl(tl(zeros))))) -> c16(MARK(adx(tl(tl(zeros))))) MARK(hd(adx(tl(adx(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) MARK(hd(adx(tl(incr(0))))) -> c16(MARK(adx(tl(incr(0))))) MARK(hd(incr(incr(y0)))) -> c16(MARK(incr(incr(y0)))) MARK(hd(incr(hd(cons(y0, y1))))) -> c16(MARK(incr(hd(cons(y0, y1))))) MARK(hd(incr(tl(cons(y0, y1))))) -> c16(MARK(incr(tl(cons(y0, y1))))) MARK(hd(incr(hd(adx(adx(y0)))))) -> c16(MARK(incr(hd(adx(adx(y0)))))) MARK(hd(incr(hd(adx(incr(y0)))))) -> c16(MARK(incr(hd(adx(incr(y0)))))) MARK(hd(incr(hd(adx(hd(y0)))))) -> c16(MARK(incr(hd(adx(hd(y0)))))) MARK(hd(incr(hd(adx(tl(y0)))))) -> c16(MARK(incr(hd(adx(tl(y0)))))) MARK(hd(incr(hd(adx(y0))))) -> c16(MARK(incr(hd(adx(y0))))) MARK(hd(incr(hd(incr(nats))))) -> c16(MARK(incr(hd(incr(nats))))) MARK(hd(incr(hd(incr(adx(y0)))))) -> c16(MARK(incr(hd(incr(adx(y0)))))) MARK(hd(incr(hd(incr(zeros))))) -> c16(MARK(incr(hd(incr(zeros))))) MARK(hd(incr(hd(incr(incr(y0)))))) -> c16(MARK(incr(hd(incr(incr(y0)))))) MARK(hd(incr(hd(incr(hd(y0)))))) -> c16(MARK(incr(hd(incr(hd(y0)))))) MARK(hd(incr(hd(incr(tl(y0)))))) -> c16(MARK(incr(hd(incr(tl(y0)))))) MARK(hd(incr(hd(incr(cons(y0, y1)))))) -> c16(MARK(incr(hd(incr(cons(y0, y1)))))) MARK(hd(incr(hd(incr(y0))))) -> c16(MARK(incr(hd(incr(y0))))) MARK(hd(incr(hd(hd(nats))))) -> c16(MARK(incr(hd(hd(nats))))) MARK(hd(incr(hd(hd(adx(y0)))))) -> c16(MARK(incr(hd(hd(adx(y0)))))) MARK(hd(incr(hd(hd(incr(y0)))))) -> c16(MARK(incr(hd(hd(incr(y0)))))) MARK(hd(incr(hd(hd(hd(y0)))))) -> c16(MARK(incr(hd(hd(hd(y0)))))) MARK(hd(incr(hd(hd(tl(y0)))))) -> c16(MARK(incr(hd(hd(tl(y0)))))) MARK(hd(incr(hd(hd(cons(y0, y1)))))) -> c16(MARK(incr(hd(hd(cons(y0, y1)))))) MARK(hd(incr(hd(hd(y0))))) -> c16(MARK(incr(hd(hd(y0))))) MARK(hd(incr(hd(tl(nats))))) -> c16(MARK(incr(hd(tl(nats))))) MARK(hd(incr(hd(tl(adx(y0)))))) -> c16(MARK(incr(hd(tl(adx(y0)))))) MARK(hd(incr(hd(tl(incr(y0)))))) -> c16(MARK(incr(hd(tl(incr(y0)))))) MARK(hd(incr(hd(tl(hd(y0)))))) -> c16(MARK(incr(hd(tl(hd(y0)))))) MARK(hd(incr(hd(tl(tl(y0)))))) -> c16(MARK(incr(hd(tl(tl(y0)))))) MARK(hd(incr(hd(tl(cons(y0, y1)))))) -> c16(MARK(incr(hd(tl(cons(y0, y1)))))) MARK(hd(incr(hd(tl(y0))))) -> c16(MARK(incr(hd(tl(y0))))) MARK(hd(incr(hd(nats)))) -> c16(MARK(incr(hd(nats)))) MARK(hd(incr(tl(adx(adx(y0)))))) -> c16(MARK(incr(tl(adx(adx(y0)))))) MARK(hd(incr(tl(adx(incr(y0)))))) -> c16(MARK(incr(tl(adx(incr(y0)))))) MARK(hd(incr(tl(adx(hd(y0)))))) -> c16(MARK(incr(tl(adx(hd(y0)))))) MARK(hd(incr(tl(adx(tl(y0)))))) -> c16(MARK(incr(tl(adx(tl(y0)))))) MARK(hd(incr(tl(adx(y0))))) -> c16(MARK(incr(tl(adx(y0))))) MARK(hd(incr(tl(incr(nats))))) -> c16(MARK(incr(tl(incr(nats))))) MARK(hd(incr(tl(incr(adx(y0)))))) -> c16(MARK(incr(tl(incr(adx(y0)))))) MARK(hd(incr(tl(incr(zeros))))) -> c16(MARK(incr(tl(incr(zeros))))) MARK(hd(incr(tl(incr(incr(y0)))))) -> c16(MARK(incr(tl(incr(incr(y0)))))) MARK(hd(incr(tl(incr(hd(y0)))))) -> c16(MARK(incr(tl(incr(hd(y0)))))) MARK(hd(incr(tl(incr(tl(y0)))))) -> c16(MARK(incr(tl(incr(tl(y0)))))) MARK(hd(incr(tl(incr(cons(y0, y1)))))) -> c16(MARK(incr(tl(incr(cons(y0, y1)))))) MARK(hd(incr(tl(incr(y0))))) -> c16(MARK(incr(tl(incr(y0))))) MARK(hd(incr(tl(hd(nats))))) -> c16(MARK(incr(tl(hd(nats))))) MARK(hd(incr(tl(hd(adx(y0)))))) -> c16(MARK(incr(tl(hd(adx(y0)))))) MARK(hd(incr(tl(hd(incr(y0)))))) -> c16(MARK(incr(tl(hd(incr(y0)))))) MARK(hd(incr(tl(hd(hd(y0)))))) -> c16(MARK(incr(tl(hd(hd(y0)))))) MARK(hd(incr(tl(hd(tl(y0)))))) -> c16(MARK(incr(tl(hd(tl(y0)))))) MARK(hd(incr(tl(hd(cons(y0, y1)))))) -> c16(MARK(incr(tl(hd(cons(y0, y1)))))) MARK(hd(incr(tl(hd(y0))))) -> c16(MARK(incr(tl(hd(y0))))) MARK(hd(incr(tl(tl(nats))))) -> c16(MARK(incr(tl(tl(nats))))) MARK(hd(incr(tl(tl(adx(y0)))))) -> c16(MARK(incr(tl(tl(adx(y0)))))) MARK(hd(incr(tl(tl(incr(y0)))))) -> c16(MARK(incr(tl(tl(incr(y0)))))) MARK(hd(incr(tl(tl(hd(y0)))))) -> c16(MARK(incr(tl(tl(hd(y0)))))) MARK(hd(incr(tl(tl(tl(y0)))))) -> c16(MARK(incr(tl(tl(tl(y0)))))) MARK(hd(incr(tl(tl(cons(y0, y1)))))) -> c16(MARK(incr(tl(tl(cons(y0, y1)))))) MARK(hd(incr(tl(tl(y0))))) -> c16(MARK(incr(tl(tl(y0))))) MARK(hd(incr(tl(nats)))) -> c16(MARK(incr(tl(nats)))) MARK(hd(incr(hd(incr(0))))) -> c16(MARK(incr(hd(incr(0))))) MARK(hd(incr(hd(incr(s(y0)))))) -> c16(MARK(incr(hd(incr(s(y0)))))) MARK(hd(incr(hd(hd(zeros))))) -> c16(MARK(incr(hd(hd(zeros))))) MARK(hd(incr(tl(hd(zeros))))) -> c16(MARK(incr(tl(hd(zeros))))) MARK(hd(incr(hd(tl(zeros))))) -> c16(MARK(incr(hd(tl(zeros))))) MARK(hd(incr(tl(tl(zeros))))) -> c16(MARK(incr(tl(tl(zeros))))) MARK(hd(incr(tl(incr(0))))) -> c16(MARK(incr(tl(incr(0))))) MARK(hd(incr(adx(adx(y0))))) -> c16(MARK(incr(adx(adx(y0))))) MARK(hd(incr(adx(incr(y0))))) -> c16(MARK(incr(adx(incr(y0))))) MARK(hd(incr(adx(hd(cons(y0, y1)))))) -> c16(MARK(incr(adx(hd(cons(y0, y1)))))) MARK(hd(incr(adx(tl(cons(y0, y1)))))) -> c16(MARK(incr(adx(tl(cons(y0, y1)))))) MARK(hd(incr(adx(hd(adx(nats)))))) -> c16(MARK(incr(adx(hd(adx(nats)))))) MARK(hd(incr(adx(hd(adx(adx(y0))))))) -> c16(MARK(incr(adx(hd(adx(adx(y0))))))) MARK(hd(incr(adx(hd(adx(zeros)))))) -> c16(MARK(incr(adx(hd(adx(zeros)))))) MARK(hd(incr(adx(hd(adx(incr(y0))))))) -> c16(MARK(incr(adx(hd(adx(incr(y0))))))) MARK(hd(incr(adx(hd(adx(hd(y0))))))) -> c16(MARK(incr(adx(hd(adx(hd(y0))))))) MARK(hd(incr(adx(hd(adx(tl(y0))))))) -> c16(MARK(incr(adx(hd(adx(tl(y0))))))) MARK(hd(incr(adx(hd(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(adx(cons(y0, y1))))))) MARK(hd(incr(adx(hd(adx(y0)))))) -> c16(MARK(incr(adx(hd(adx(y0)))))) MARK(hd(incr(adx(hd(incr(nats)))))) -> c16(MARK(incr(adx(hd(incr(nats)))))) MARK(hd(incr(adx(hd(incr(adx(y0))))))) -> c16(MARK(incr(adx(hd(incr(adx(y0))))))) MARK(hd(incr(adx(hd(incr(zeros)))))) -> c16(MARK(incr(adx(hd(incr(zeros)))))) MARK(hd(incr(adx(hd(incr(incr(y0))))))) -> c16(MARK(incr(adx(hd(incr(incr(y0))))))) MARK(hd(incr(adx(hd(incr(hd(y0))))))) -> c16(MARK(incr(adx(hd(incr(hd(y0))))))) MARK(hd(incr(adx(hd(incr(tl(y0))))))) -> c16(MARK(incr(adx(hd(incr(tl(y0))))))) MARK(hd(incr(adx(hd(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(incr(cons(y0, y1))))))) MARK(hd(incr(adx(hd(incr(y0)))))) -> c16(MARK(incr(adx(hd(incr(y0)))))) MARK(hd(incr(adx(hd(hd(nats)))))) -> c16(MARK(incr(adx(hd(hd(nats)))))) MARK(hd(incr(adx(hd(hd(adx(y0))))))) -> c16(MARK(incr(adx(hd(hd(adx(y0))))))) MARK(hd(incr(adx(hd(hd(incr(y0))))))) -> c16(MARK(incr(adx(hd(hd(incr(y0))))))) MARK(hd(incr(adx(hd(hd(hd(y0))))))) -> c16(MARK(incr(adx(hd(hd(hd(y0))))))) MARK(hd(incr(adx(hd(hd(tl(y0))))))) -> c16(MARK(incr(adx(hd(hd(tl(y0))))))) MARK(hd(incr(adx(hd(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(hd(cons(y0, y1))))))) MARK(hd(incr(adx(hd(hd(y0)))))) -> c16(MARK(incr(adx(hd(hd(y0)))))) MARK(hd(incr(adx(hd(tl(nats)))))) -> c16(MARK(incr(adx(hd(tl(nats)))))) MARK(hd(incr(adx(hd(tl(adx(y0))))))) -> c16(MARK(incr(adx(hd(tl(adx(y0))))))) MARK(hd(incr(adx(hd(tl(incr(y0))))))) -> c16(MARK(incr(adx(hd(tl(incr(y0))))))) MARK(hd(incr(adx(hd(tl(hd(y0))))))) -> c16(MARK(incr(adx(hd(tl(hd(y0))))))) MARK(hd(incr(adx(hd(tl(tl(y0))))))) -> c16(MARK(incr(adx(hd(tl(tl(y0))))))) MARK(hd(incr(adx(hd(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(tl(cons(y0, y1))))))) MARK(hd(incr(adx(hd(tl(y0)))))) -> c16(MARK(incr(adx(hd(tl(y0)))))) MARK(hd(incr(adx(hd(nats))))) -> c16(MARK(incr(adx(hd(nats))))) MARK(hd(incr(adx(tl(adx(nats)))))) -> c16(MARK(incr(adx(tl(adx(nats)))))) MARK(hd(incr(adx(tl(adx(adx(y0))))))) -> c16(MARK(incr(adx(tl(adx(adx(y0))))))) MARK(hd(incr(adx(tl(adx(zeros)))))) -> c16(MARK(incr(adx(tl(adx(zeros)))))) MARK(hd(incr(adx(tl(adx(incr(y0))))))) -> c16(MARK(incr(adx(tl(adx(incr(y0))))))) MARK(hd(incr(adx(tl(adx(hd(y0))))))) -> c16(MARK(incr(adx(tl(adx(hd(y0))))))) MARK(hd(incr(adx(tl(adx(tl(y0))))))) -> c16(MARK(incr(adx(tl(adx(tl(y0))))))) MARK(hd(incr(adx(tl(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(adx(cons(y0, y1))))))) MARK(hd(incr(adx(tl(adx(y0)))))) -> c16(MARK(incr(adx(tl(adx(y0)))))) MARK(hd(incr(adx(tl(incr(nats)))))) -> c16(MARK(incr(adx(tl(incr(nats)))))) MARK(hd(incr(adx(tl(incr(adx(y0))))))) -> c16(MARK(incr(adx(tl(incr(adx(y0))))))) MARK(hd(incr(adx(tl(incr(zeros)))))) -> c16(MARK(incr(adx(tl(incr(zeros)))))) MARK(hd(incr(adx(tl(incr(incr(y0))))))) -> c16(MARK(incr(adx(tl(incr(incr(y0))))))) MARK(hd(incr(adx(tl(incr(hd(y0))))))) -> c16(MARK(incr(adx(tl(incr(hd(y0))))))) MARK(hd(incr(adx(tl(incr(tl(y0))))))) -> c16(MARK(incr(adx(tl(incr(tl(y0))))))) MARK(hd(incr(adx(tl(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(incr(cons(y0, y1))))))) MARK(hd(incr(adx(tl(incr(s(y0))))))) -> c16(MARK(incr(adx(tl(incr(s(y0))))))) MARK(hd(incr(adx(tl(incr(y0)))))) -> c16(MARK(incr(adx(tl(incr(y0)))))) MARK(hd(incr(adx(tl(hd(nats)))))) -> c16(MARK(incr(adx(tl(hd(nats)))))) MARK(hd(incr(adx(tl(hd(adx(y0))))))) -> c16(MARK(incr(adx(tl(hd(adx(y0))))))) MARK(hd(incr(adx(tl(hd(incr(y0))))))) -> c16(MARK(incr(adx(tl(hd(incr(y0))))))) MARK(hd(incr(adx(tl(hd(hd(y0))))))) -> c16(MARK(incr(adx(tl(hd(hd(y0))))))) MARK(hd(incr(adx(tl(hd(tl(y0))))))) -> c16(MARK(incr(adx(tl(hd(tl(y0))))))) MARK(hd(incr(adx(tl(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(hd(cons(y0, y1))))))) MARK(hd(incr(adx(tl(hd(y0)))))) -> c16(MARK(incr(adx(tl(hd(y0)))))) MARK(hd(incr(adx(tl(tl(nats)))))) -> c16(MARK(incr(adx(tl(tl(nats)))))) MARK(hd(incr(adx(tl(tl(adx(y0))))))) -> c16(MARK(incr(adx(tl(tl(adx(y0))))))) MARK(hd(incr(adx(tl(tl(incr(y0))))))) -> c16(MARK(incr(adx(tl(tl(incr(y0))))))) MARK(hd(incr(adx(tl(tl(hd(y0))))))) -> c16(MARK(incr(adx(tl(tl(hd(y0))))))) MARK(hd(incr(adx(tl(tl(tl(y0))))))) -> c16(MARK(incr(adx(tl(tl(tl(y0))))))) MARK(hd(incr(adx(tl(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(tl(cons(y0, y1))))))) MARK(hd(incr(adx(tl(tl(y0)))))) -> c16(MARK(incr(adx(tl(tl(y0)))))) MARK(hd(incr(adx(tl(nats))))) -> c16(MARK(incr(adx(tl(nats))))) MARK(hd(incr(adx(hd(adx(0)))))) -> c16(MARK(incr(adx(hd(adx(0)))))) MARK(hd(incr(adx(hd(adx(s(y0))))))) -> c16(MARK(incr(adx(hd(adx(s(y0))))))) MARK(hd(incr(adx(hd(incr(0)))))) -> c16(MARK(incr(adx(hd(incr(0)))))) MARK(hd(incr(adx(hd(incr(s(y0))))))) -> c16(MARK(incr(adx(hd(incr(s(y0))))))) MARK(hd(incr(adx(hd(hd(zeros)))))) -> c16(MARK(incr(adx(hd(hd(zeros)))))) MARK(hd(incr(adx(tl(hd(zeros)))))) -> c16(MARK(incr(adx(tl(hd(zeros)))))) MARK(hd(incr(adx(tl(adx(0)))))) -> c16(MARK(incr(adx(tl(adx(0)))))) MARK(hd(incr(adx(hd(tl(zeros)))))) -> c16(MARK(incr(adx(hd(tl(zeros)))))) MARK(hd(incr(adx(tl(tl(zeros)))))) -> c16(MARK(incr(adx(tl(tl(zeros)))))) MARK(hd(incr(adx(tl(adx(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) MARK(hd(incr(adx(tl(incr(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) MARK(hd(incr(hd(adx(nats))))) -> c16(MARK(incr(hd(adx(nats))))) MARK(hd(incr(hd(adx(zeros))))) -> c16(MARK(incr(hd(adx(zeros))))) MARK(hd(incr(hd(adx(cons(y0, y1)))))) -> c16(MARK(incr(hd(adx(cons(y0, y1)))))) MARK(hd(incr(tl(adx(nats))))) -> c16(MARK(incr(tl(adx(nats))))) MARK(hd(incr(tl(adx(zeros))))) -> c16(MARK(incr(tl(adx(zeros))))) MARK(hd(incr(tl(adx(cons(y0, y1)))))) -> c16(MARK(incr(tl(adx(cons(y0, y1)))))) MARK(hd(incr(tl(incr(s(y0)))))) -> c16(MARK(incr(tl(incr(s(y0)))))) S tuples: MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) A__HD(cons(hd(incr(s(y0))), z1)) -> 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A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) MARK(tl(cons(z0, adx(y1)))) -> c17(A__TL(cons(z0, adx(y1)))) MARK(tl(cons(z0, incr(y1)))) -> c17(A__TL(cons(z0, incr(y1)))) MARK(tl(cons(z0, hd(cons(y1, y2))))) -> c17(A__TL(cons(z0, hd(cons(y1, y2))))) MARK(tl(cons(z0, tl(cons(y1, y2))))) -> c17(A__TL(cons(z0, tl(cons(y1, y2))))) MARK(tl(cons(z0, hd(adx(nats))))) -> c17(A__TL(cons(z0, hd(adx(nats))))) MARK(tl(cons(z0, hd(adx(adx(y1)))))) -> c17(A__TL(cons(z0, hd(adx(adx(y1)))))) MARK(tl(cons(z0, hd(adx(zeros))))) -> c17(A__TL(cons(z0, hd(adx(zeros))))) MARK(tl(cons(z0, hd(adx(incr(y1)))))) -> c17(A__TL(cons(z0, hd(adx(incr(y1)))))) MARK(tl(cons(z0, hd(adx(hd(y1)))))) -> c17(A__TL(cons(z0, hd(adx(hd(y1)))))) MARK(tl(cons(z0, hd(adx(tl(y1)))))) -> c17(A__TL(cons(z0, hd(adx(tl(y1)))))) MARK(tl(cons(z0, hd(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(adx(cons(y1, y2)))))) MARK(tl(cons(z0, hd(adx(y1))))) -> c17(A__TL(cons(z0, hd(adx(y1))))) MARK(tl(cons(z0, hd(incr(nats))))) -> c17(A__TL(cons(z0, hd(incr(nats))))) MARK(tl(cons(z0, hd(incr(adx(y1)))))) -> c17(A__TL(cons(z0, hd(incr(adx(y1)))))) MARK(tl(cons(z0, hd(incr(zeros))))) -> c17(A__TL(cons(z0, hd(incr(zeros))))) MARK(tl(cons(z0, hd(incr(incr(y1)))))) -> c17(A__TL(cons(z0, hd(incr(incr(y1)))))) MARK(tl(cons(z0, hd(incr(hd(y1)))))) -> c17(A__TL(cons(z0, hd(incr(hd(y1)))))) MARK(tl(cons(z0, hd(incr(tl(y1)))))) -> c17(A__TL(cons(z0, hd(incr(tl(y1)))))) MARK(tl(cons(z0, hd(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(incr(cons(y1, y2)))))) MARK(tl(cons(z0, hd(incr(y1))))) -> c17(A__TL(cons(z0, hd(incr(y1))))) MARK(tl(cons(z0, hd(hd(nats))))) -> c17(A__TL(cons(z0, hd(hd(nats))))) MARK(tl(cons(z0, hd(hd(adx(y1)))))) -> c17(A__TL(cons(z0, hd(hd(adx(y1)))))) MARK(tl(cons(z0, hd(hd(incr(y1)))))) -> c17(A__TL(cons(z0, hd(hd(incr(y1)))))) MARK(tl(cons(z0, hd(hd(hd(y1)))))) -> c17(A__TL(cons(z0, hd(hd(hd(y1)))))) MARK(tl(cons(z0, hd(hd(tl(y1)))))) -> c17(A__TL(cons(z0, hd(hd(tl(y1)))))) MARK(tl(cons(z0, hd(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(hd(cons(y1, y2)))))) MARK(tl(cons(z0, hd(hd(y1))))) -> c17(A__TL(cons(z0, hd(hd(y1))))) MARK(tl(cons(z0, hd(tl(nats))))) -> c17(A__TL(cons(z0, hd(tl(nats))))) MARK(tl(cons(z0, hd(tl(adx(y1)))))) -> c17(A__TL(cons(z0, hd(tl(adx(y1)))))) MARK(tl(cons(z0, hd(tl(zeros))))) -> c17(A__TL(cons(z0, hd(tl(zeros))))) MARK(tl(cons(z0, hd(tl(incr(y1)))))) -> c17(A__TL(cons(z0, hd(tl(incr(y1)))))) MARK(tl(cons(z0, hd(tl(hd(y1)))))) -> c17(A__TL(cons(z0, hd(tl(hd(y1)))))) MARK(tl(cons(z0, hd(tl(tl(y1)))))) -> c17(A__TL(cons(z0, hd(tl(tl(y1)))))) MARK(tl(cons(z0, hd(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(tl(cons(y1, y2)))))) MARK(tl(cons(z0, hd(tl(y1))))) -> c17(A__TL(cons(z0, hd(tl(y1))))) MARK(tl(cons(z0, hd(nats)))) -> c17(A__TL(cons(z0, hd(nats)))) MARK(tl(cons(z0, tl(adx(nats))))) -> c17(A__TL(cons(z0, tl(adx(nats))))) MARK(tl(cons(z0, tl(adx(adx(y1)))))) -> c17(A__TL(cons(z0, tl(adx(adx(y1)))))) MARK(tl(cons(z0, tl(adx(zeros))))) -> c17(A__TL(cons(z0, tl(adx(zeros))))) MARK(tl(cons(z0, tl(adx(incr(y1)))))) -> c17(A__TL(cons(z0, tl(adx(incr(y1)))))) MARK(tl(cons(z0, tl(adx(hd(y1)))))) -> c17(A__TL(cons(z0, tl(adx(hd(y1)))))) MARK(tl(cons(z0, tl(adx(tl(y1)))))) -> c17(A__TL(cons(z0, tl(adx(tl(y1)))))) MARK(tl(cons(z0, tl(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(adx(cons(y1, y2)))))) MARK(tl(cons(z0, tl(adx(s(y1)))))) -> c17(A__TL(cons(z0, tl(adx(s(y1)))))) MARK(tl(cons(z0, tl(adx(y1))))) -> c17(A__TL(cons(z0, tl(adx(y1))))) MARK(tl(cons(z0, tl(incr(nats))))) -> c17(A__TL(cons(z0, tl(incr(nats))))) MARK(tl(cons(z0, tl(incr(adx(y1)))))) -> c17(A__TL(cons(z0, tl(incr(adx(y1)))))) MARK(tl(cons(z0, tl(incr(zeros))))) -> c17(A__TL(cons(z0, tl(incr(zeros))))) MARK(tl(cons(z0, tl(incr(incr(y1)))))) -> c17(A__TL(cons(z0, tl(incr(incr(y1)))))) MARK(tl(cons(z0, tl(incr(hd(y1)))))) -> c17(A__TL(cons(z0, tl(incr(hd(y1)))))) MARK(tl(cons(z0, tl(incr(tl(y1)))))) -> c17(A__TL(cons(z0, tl(incr(tl(y1)))))) MARK(tl(cons(z0, tl(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(incr(cons(y1, y2)))))) MARK(tl(cons(z0, tl(incr(0))))) -> c17(A__TL(cons(z0, tl(incr(0))))) MARK(tl(cons(z0, tl(incr(s(y1)))))) -> c17(A__TL(cons(z0, tl(incr(s(y1)))))) MARK(tl(cons(z0, tl(incr(y1))))) -> c17(A__TL(cons(z0, tl(incr(y1))))) MARK(tl(cons(z0, tl(hd(nats))))) -> c17(A__TL(cons(z0, tl(hd(nats))))) MARK(tl(cons(z0, tl(hd(adx(y1)))))) -> c17(A__TL(cons(z0, tl(hd(adx(y1)))))) MARK(tl(cons(z0, tl(hd(incr(y1)))))) -> c17(A__TL(cons(z0, tl(hd(incr(y1)))))) MARK(tl(cons(z0, tl(hd(hd(y1)))))) -> c17(A__TL(cons(z0, tl(hd(hd(y1)))))) MARK(tl(cons(z0, tl(hd(tl(y1)))))) -> c17(A__TL(cons(z0, tl(hd(tl(y1)))))) MARK(tl(cons(z0, tl(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(hd(cons(y1, y2)))))) MARK(tl(cons(z0, tl(hd(y1))))) -> c17(A__TL(cons(z0, tl(hd(y1))))) MARK(tl(cons(z0, tl(tl(nats))))) -> c17(A__TL(cons(z0, tl(tl(nats))))) MARK(tl(cons(z0, tl(tl(adx(y1)))))) -> c17(A__TL(cons(z0, tl(tl(adx(y1)))))) MARK(tl(cons(z0, tl(tl(zeros))))) -> c17(A__TL(cons(z0, tl(tl(zeros))))) MARK(tl(cons(z0, tl(tl(incr(y1)))))) -> c17(A__TL(cons(z0, tl(tl(incr(y1)))))) MARK(tl(cons(z0, tl(tl(hd(y1)))))) -> c17(A__TL(cons(z0, tl(tl(hd(y1)))))) MARK(tl(cons(z0, tl(tl(tl(y1)))))) -> c17(A__TL(cons(z0, tl(tl(tl(y1)))))) MARK(tl(cons(z0, tl(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(tl(cons(y1, y2)))))) MARK(tl(cons(z0, tl(tl(y1))))) -> c17(A__TL(cons(z0, tl(tl(y1))))) MARK(tl(cons(z0, tl(nats)))) -> c17(A__TL(cons(z0, tl(nats)))) MARK(tl(cons(z0, hd(adx(0))))) -> c17(A__TL(cons(z0, hd(adx(0))))) MARK(tl(cons(z0, hd(adx(s(y1)))))) -> c17(A__TL(cons(z0, hd(adx(s(y1)))))) MARK(tl(cons(z0, hd(incr(0))))) -> c17(A__TL(cons(z0, hd(incr(0))))) MARK(tl(cons(z0, hd(incr(s(y1)))))) -> c17(A__TL(cons(z0, hd(incr(s(y1)))))) MARK(tl(cons(z0, hd(hd(zeros))))) -> c17(A__TL(cons(z0, hd(hd(zeros))))) MARK(tl(cons(z0, tl(hd(zeros))))) -> c17(A__TL(cons(z0, tl(hd(zeros))))) MARK(tl(cons(z0, tl(adx(0))))) -> c17(A__TL(cons(z0, tl(adx(0))))) MARK(hd(adx(adx(y0)))) -> c16(MARK(adx(adx(y0)))) MARK(hd(adx(incr(y0)))) -> c16(MARK(adx(incr(y0)))) MARK(hd(adx(hd(cons(y0, y1))))) -> c16(MARK(adx(hd(cons(y0, y1))))) MARK(hd(adx(tl(cons(y0, y1))))) -> c16(MARK(adx(tl(cons(y0, y1))))) MARK(hd(adx(hd(adx(nats))))) -> c16(MARK(adx(hd(adx(nats))))) MARK(hd(adx(hd(adx(adx(y0)))))) -> c16(MARK(adx(hd(adx(adx(y0)))))) MARK(hd(adx(hd(adx(zeros))))) -> c16(MARK(adx(hd(adx(zeros))))) MARK(hd(adx(hd(adx(incr(y0)))))) -> c16(MARK(adx(hd(adx(incr(y0)))))) MARK(hd(adx(hd(adx(hd(y0)))))) -> c16(MARK(adx(hd(adx(hd(y0)))))) MARK(hd(adx(hd(adx(tl(y0)))))) -> c16(MARK(adx(hd(adx(tl(y0)))))) MARK(hd(adx(hd(adx(cons(y0, y1)))))) -> c16(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(hd(adx(hd(adx(y0))))) -> c16(MARK(adx(hd(adx(y0))))) MARK(hd(adx(hd(incr(nats))))) -> c16(MARK(adx(hd(incr(nats))))) MARK(hd(adx(hd(incr(adx(y0)))))) -> c16(MARK(adx(hd(incr(adx(y0)))))) MARK(hd(adx(hd(incr(zeros))))) -> c16(MARK(adx(hd(incr(zeros))))) MARK(hd(adx(hd(incr(incr(y0)))))) -> c16(MARK(adx(hd(incr(incr(y0)))))) MARK(hd(adx(hd(incr(hd(y0)))))) -> c16(MARK(adx(hd(incr(hd(y0)))))) MARK(hd(adx(hd(incr(tl(y0)))))) -> c16(MARK(adx(hd(incr(tl(y0)))))) MARK(hd(adx(hd(incr(cons(y0, y1)))))) -> c16(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(hd(adx(hd(incr(y0))))) -> c16(MARK(adx(hd(incr(y0))))) MARK(hd(adx(hd(hd(nats))))) -> c16(MARK(adx(hd(hd(nats))))) MARK(hd(adx(hd(hd(adx(y0)))))) -> c16(MARK(adx(hd(hd(adx(y0)))))) MARK(hd(adx(hd(hd(incr(y0)))))) -> c16(MARK(adx(hd(hd(incr(y0)))))) MARK(hd(adx(hd(hd(hd(y0)))))) -> c16(MARK(adx(hd(hd(hd(y0)))))) MARK(hd(adx(hd(hd(tl(y0)))))) -> c16(MARK(adx(hd(hd(tl(y0)))))) MARK(hd(adx(hd(hd(cons(y0, y1)))))) -> c16(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(hd(adx(hd(hd(y0))))) -> c16(MARK(adx(hd(hd(y0))))) MARK(hd(adx(hd(tl(nats))))) -> c16(MARK(adx(hd(tl(nats))))) MARK(hd(adx(hd(tl(adx(y0)))))) -> c16(MARK(adx(hd(tl(adx(y0)))))) MARK(hd(adx(hd(tl(incr(y0)))))) -> c16(MARK(adx(hd(tl(incr(y0)))))) MARK(hd(adx(hd(tl(hd(y0)))))) -> c16(MARK(adx(hd(tl(hd(y0)))))) MARK(hd(adx(hd(tl(tl(y0)))))) -> c16(MARK(adx(hd(tl(tl(y0)))))) MARK(hd(adx(hd(tl(cons(y0, y1)))))) -> c16(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(hd(adx(hd(tl(y0))))) -> c16(MARK(adx(hd(tl(y0))))) MARK(hd(adx(hd(nats)))) -> c16(MARK(adx(hd(nats)))) MARK(hd(adx(tl(adx(nats))))) -> c16(MARK(adx(tl(adx(nats))))) MARK(hd(adx(tl(adx(adx(y0)))))) -> c16(MARK(adx(tl(adx(adx(y0)))))) MARK(hd(adx(tl(adx(zeros))))) -> c16(MARK(adx(tl(adx(zeros))))) MARK(hd(adx(tl(adx(incr(y0)))))) -> c16(MARK(adx(tl(adx(incr(y0)))))) MARK(hd(adx(tl(adx(hd(y0)))))) -> c16(MARK(adx(tl(adx(hd(y0)))))) MARK(hd(adx(tl(adx(tl(y0)))))) -> c16(MARK(adx(tl(adx(tl(y0)))))) MARK(hd(adx(tl(adx(cons(y0, y1)))))) -> c16(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(hd(adx(tl(adx(y0))))) -> c16(MARK(adx(tl(adx(y0))))) MARK(hd(adx(tl(incr(nats))))) -> c16(MARK(adx(tl(incr(nats))))) MARK(hd(adx(tl(incr(adx(y0)))))) -> c16(MARK(adx(tl(incr(adx(y0)))))) MARK(hd(adx(tl(incr(zeros))))) -> c16(MARK(adx(tl(incr(zeros))))) MARK(hd(adx(tl(incr(incr(y0)))))) -> c16(MARK(adx(tl(incr(incr(y0)))))) MARK(hd(adx(tl(incr(hd(y0)))))) -> c16(MARK(adx(tl(incr(hd(y0)))))) MARK(hd(adx(tl(incr(tl(y0)))))) -> c16(MARK(adx(tl(incr(tl(y0)))))) MARK(hd(adx(tl(incr(cons(y0, y1)))))) -> c16(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(hd(adx(tl(incr(s(y0)))))) -> c16(MARK(adx(tl(incr(s(y0)))))) MARK(hd(adx(tl(incr(y0))))) -> c16(MARK(adx(tl(incr(y0))))) MARK(hd(adx(tl(hd(nats))))) -> c16(MARK(adx(tl(hd(nats))))) MARK(hd(adx(tl(hd(adx(y0)))))) -> c16(MARK(adx(tl(hd(adx(y0)))))) MARK(hd(adx(tl(hd(incr(y0)))))) -> c16(MARK(adx(tl(hd(incr(y0)))))) MARK(hd(adx(tl(hd(hd(y0)))))) -> c16(MARK(adx(tl(hd(hd(y0)))))) MARK(hd(adx(tl(hd(tl(y0)))))) -> c16(MARK(adx(tl(hd(tl(y0)))))) MARK(hd(adx(tl(hd(cons(y0, y1)))))) -> c16(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(hd(adx(tl(hd(y0))))) -> c16(MARK(adx(tl(hd(y0))))) MARK(hd(adx(tl(tl(nats))))) -> c16(MARK(adx(tl(tl(nats))))) MARK(hd(adx(tl(tl(adx(y0)))))) -> c16(MARK(adx(tl(tl(adx(y0)))))) MARK(hd(adx(tl(tl(incr(y0)))))) -> c16(MARK(adx(tl(tl(incr(y0)))))) MARK(hd(adx(tl(tl(hd(y0)))))) -> c16(MARK(adx(tl(tl(hd(y0)))))) MARK(hd(adx(tl(tl(tl(y0)))))) -> c16(MARK(adx(tl(tl(tl(y0)))))) MARK(hd(adx(tl(tl(cons(y0, y1)))))) -> c16(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(hd(adx(tl(tl(y0))))) -> c16(MARK(adx(tl(tl(y0))))) MARK(hd(adx(tl(nats)))) -> c16(MARK(adx(tl(nats)))) MARK(hd(adx(hd(adx(0))))) -> c16(MARK(adx(hd(adx(0))))) MARK(hd(adx(hd(adx(s(y0)))))) -> c16(MARK(adx(hd(adx(s(y0)))))) MARK(hd(adx(hd(incr(0))))) -> c16(MARK(adx(hd(incr(0))))) MARK(hd(adx(hd(incr(s(y0)))))) -> c16(MARK(adx(hd(incr(s(y0)))))) MARK(hd(adx(hd(hd(zeros))))) -> c16(MARK(adx(hd(hd(zeros))))) MARK(hd(adx(tl(hd(zeros))))) -> c16(MARK(adx(tl(hd(zeros))))) MARK(hd(adx(tl(adx(0))))) -> c16(MARK(adx(tl(adx(0))))) MARK(hd(adx(hd(tl(zeros))))) -> c16(MARK(adx(hd(tl(zeros))))) MARK(hd(adx(tl(tl(zeros))))) -> c16(MARK(adx(tl(tl(zeros))))) MARK(hd(adx(tl(adx(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) MARK(hd(adx(tl(incr(0))))) -> c16(MARK(adx(tl(incr(0))))) MARK(hd(incr(incr(y0)))) -> c16(MARK(incr(incr(y0)))) MARK(hd(incr(hd(cons(y0, y1))))) -> c16(MARK(incr(hd(cons(y0, y1))))) MARK(hd(incr(tl(cons(y0, y1))))) -> c16(MARK(incr(tl(cons(y0, y1))))) MARK(hd(incr(hd(adx(adx(y0)))))) -> c16(MARK(incr(hd(adx(adx(y0)))))) MARK(hd(incr(hd(adx(incr(y0)))))) -> c16(MARK(incr(hd(adx(incr(y0)))))) MARK(hd(incr(hd(adx(hd(y0)))))) -> c16(MARK(incr(hd(adx(hd(y0)))))) MARK(hd(incr(hd(adx(tl(y0)))))) -> c16(MARK(incr(hd(adx(tl(y0)))))) MARK(hd(incr(hd(adx(y0))))) -> c16(MARK(incr(hd(adx(y0))))) MARK(hd(incr(hd(incr(nats))))) -> c16(MARK(incr(hd(incr(nats))))) MARK(hd(incr(hd(incr(adx(y0)))))) -> c16(MARK(incr(hd(incr(adx(y0)))))) MARK(hd(incr(hd(incr(zeros))))) -> c16(MARK(incr(hd(incr(zeros))))) MARK(hd(incr(hd(incr(incr(y0)))))) -> c16(MARK(incr(hd(incr(incr(y0)))))) MARK(hd(incr(hd(incr(hd(y0)))))) -> c16(MARK(incr(hd(incr(hd(y0)))))) MARK(hd(incr(hd(incr(tl(y0)))))) -> c16(MARK(incr(hd(incr(tl(y0)))))) MARK(hd(incr(hd(incr(cons(y0, y1)))))) -> c16(MARK(incr(hd(incr(cons(y0, y1)))))) MARK(hd(incr(hd(incr(y0))))) -> c16(MARK(incr(hd(incr(y0))))) MARK(hd(incr(hd(hd(nats))))) -> c16(MARK(incr(hd(hd(nats))))) MARK(hd(incr(hd(hd(adx(y0)))))) -> c16(MARK(incr(hd(hd(adx(y0)))))) MARK(hd(incr(hd(hd(incr(y0)))))) -> c16(MARK(incr(hd(hd(incr(y0)))))) MARK(hd(incr(hd(hd(hd(y0)))))) -> c16(MARK(incr(hd(hd(hd(y0)))))) MARK(hd(incr(hd(hd(tl(y0)))))) -> c16(MARK(incr(hd(hd(tl(y0)))))) MARK(hd(incr(hd(hd(cons(y0, y1)))))) -> c16(MARK(incr(hd(hd(cons(y0, y1)))))) MARK(hd(incr(hd(hd(y0))))) -> c16(MARK(incr(hd(hd(y0))))) MARK(hd(incr(hd(tl(nats))))) -> c16(MARK(incr(hd(tl(nats))))) MARK(hd(incr(hd(tl(adx(y0)))))) -> c16(MARK(incr(hd(tl(adx(y0)))))) MARK(hd(incr(hd(tl(incr(y0)))))) -> c16(MARK(incr(hd(tl(incr(y0)))))) MARK(hd(incr(hd(tl(hd(y0)))))) -> c16(MARK(incr(hd(tl(hd(y0)))))) MARK(hd(incr(hd(tl(tl(y0)))))) -> c16(MARK(incr(hd(tl(tl(y0)))))) MARK(hd(incr(hd(tl(cons(y0, y1)))))) -> c16(MARK(incr(hd(tl(cons(y0, y1)))))) MARK(hd(incr(hd(tl(y0))))) -> c16(MARK(incr(hd(tl(y0))))) MARK(hd(incr(hd(nats)))) -> c16(MARK(incr(hd(nats)))) MARK(hd(incr(tl(adx(adx(y0)))))) -> c16(MARK(incr(tl(adx(adx(y0)))))) MARK(hd(incr(tl(adx(incr(y0)))))) -> c16(MARK(incr(tl(adx(incr(y0)))))) MARK(hd(incr(tl(adx(hd(y0)))))) -> c16(MARK(incr(tl(adx(hd(y0)))))) MARK(hd(incr(tl(adx(tl(y0)))))) -> c16(MARK(incr(tl(adx(tl(y0)))))) MARK(hd(incr(tl(adx(y0))))) -> c16(MARK(incr(tl(adx(y0))))) MARK(hd(incr(tl(incr(nats))))) -> c16(MARK(incr(tl(incr(nats))))) MARK(hd(incr(tl(incr(adx(y0)))))) -> c16(MARK(incr(tl(incr(adx(y0)))))) MARK(hd(incr(tl(incr(zeros))))) -> c16(MARK(incr(tl(incr(zeros))))) MARK(hd(incr(tl(incr(incr(y0)))))) -> c16(MARK(incr(tl(incr(incr(y0)))))) MARK(hd(incr(tl(incr(hd(y0)))))) -> c16(MARK(incr(tl(incr(hd(y0)))))) MARK(hd(incr(tl(incr(tl(y0)))))) -> c16(MARK(incr(tl(incr(tl(y0)))))) MARK(hd(incr(tl(incr(cons(y0, y1)))))) -> c16(MARK(incr(tl(incr(cons(y0, y1)))))) MARK(hd(incr(tl(incr(y0))))) -> c16(MARK(incr(tl(incr(y0))))) MARK(hd(incr(tl(hd(nats))))) -> c16(MARK(incr(tl(hd(nats))))) MARK(hd(incr(tl(hd(adx(y0)))))) -> c16(MARK(incr(tl(hd(adx(y0)))))) MARK(hd(incr(tl(hd(incr(y0)))))) -> c16(MARK(incr(tl(hd(incr(y0)))))) MARK(hd(incr(tl(hd(hd(y0)))))) -> c16(MARK(incr(tl(hd(hd(y0)))))) MARK(hd(incr(tl(hd(tl(y0)))))) -> c16(MARK(incr(tl(hd(tl(y0)))))) MARK(hd(incr(tl(hd(cons(y0, y1)))))) -> c16(MARK(incr(tl(hd(cons(y0, y1)))))) MARK(hd(incr(tl(hd(y0))))) -> c16(MARK(incr(tl(hd(y0))))) MARK(hd(incr(tl(tl(nats))))) -> c16(MARK(incr(tl(tl(nats))))) MARK(hd(incr(tl(tl(adx(y0)))))) -> c16(MARK(incr(tl(tl(adx(y0)))))) MARK(hd(incr(tl(tl(incr(y0)))))) -> c16(MARK(incr(tl(tl(incr(y0)))))) MARK(hd(incr(tl(tl(hd(y0)))))) -> c16(MARK(incr(tl(tl(hd(y0)))))) MARK(hd(incr(tl(tl(tl(y0)))))) -> c16(MARK(incr(tl(tl(tl(y0)))))) MARK(hd(incr(tl(tl(cons(y0, y1)))))) -> c16(MARK(incr(tl(tl(cons(y0, y1)))))) MARK(hd(incr(tl(tl(y0))))) -> c16(MARK(incr(tl(tl(y0))))) MARK(hd(incr(tl(nats)))) -> c16(MARK(incr(tl(nats)))) MARK(hd(incr(hd(incr(0))))) -> c16(MARK(incr(hd(incr(0))))) MARK(hd(incr(hd(incr(s(y0)))))) -> c16(MARK(incr(hd(incr(s(y0)))))) MARK(hd(incr(hd(hd(zeros))))) -> c16(MARK(incr(hd(hd(zeros))))) MARK(hd(incr(tl(hd(zeros))))) -> c16(MARK(incr(tl(hd(zeros))))) MARK(hd(incr(hd(tl(zeros))))) -> c16(MARK(incr(hd(tl(zeros))))) MARK(hd(incr(tl(tl(zeros))))) -> c16(MARK(incr(tl(tl(zeros))))) MARK(hd(incr(tl(incr(0))))) -> c16(MARK(incr(tl(incr(0))))) MARK(hd(incr(adx(adx(y0))))) -> c16(MARK(incr(adx(adx(y0))))) MARK(hd(incr(adx(incr(y0))))) -> c16(MARK(incr(adx(incr(y0))))) MARK(hd(incr(adx(hd(cons(y0, y1)))))) -> c16(MARK(incr(adx(hd(cons(y0, y1)))))) MARK(hd(incr(adx(tl(cons(y0, y1)))))) -> c16(MARK(incr(adx(tl(cons(y0, y1)))))) MARK(hd(incr(adx(hd(adx(nats)))))) -> c16(MARK(incr(adx(hd(adx(nats)))))) MARK(hd(incr(adx(hd(adx(adx(y0))))))) -> c16(MARK(incr(adx(hd(adx(adx(y0))))))) MARK(hd(incr(adx(hd(adx(zeros)))))) -> c16(MARK(incr(adx(hd(adx(zeros)))))) MARK(hd(incr(adx(hd(adx(incr(y0))))))) -> c16(MARK(incr(adx(hd(adx(incr(y0))))))) MARK(hd(incr(adx(hd(adx(hd(y0))))))) -> c16(MARK(incr(adx(hd(adx(hd(y0))))))) MARK(hd(incr(adx(hd(adx(tl(y0))))))) -> c16(MARK(incr(adx(hd(adx(tl(y0))))))) MARK(hd(incr(adx(hd(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(adx(cons(y0, y1))))))) MARK(hd(incr(adx(hd(adx(y0)))))) -> c16(MARK(incr(adx(hd(adx(y0)))))) MARK(hd(incr(adx(hd(incr(nats)))))) -> c16(MARK(incr(adx(hd(incr(nats)))))) MARK(hd(incr(adx(hd(incr(adx(y0))))))) -> c16(MARK(incr(adx(hd(incr(adx(y0))))))) MARK(hd(incr(adx(hd(incr(zeros)))))) -> c16(MARK(incr(adx(hd(incr(zeros)))))) MARK(hd(incr(adx(hd(incr(incr(y0))))))) -> c16(MARK(incr(adx(hd(incr(incr(y0))))))) MARK(hd(incr(adx(hd(incr(hd(y0))))))) -> c16(MARK(incr(adx(hd(incr(hd(y0))))))) MARK(hd(incr(adx(hd(incr(tl(y0))))))) -> c16(MARK(incr(adx(hd(incr(tl(y0))))))) MARK(hd(incr(adx(hd(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(incr(cons(y0, y1))))))) MARK(hd(incr(adx(hd(incr(y0)))))) -> c16(MARK(incr(adx(hd(incr(y0)))))) MARK(hd(incr(adx(hd(hd(nats)))))) -> c16(MARK(incr(adx(hd(hd(nats)))))) MARK(hd(incr(adx(hd(hd(adx(y0))))))) -> c16(MARK(incr(adx(hd(hd(adx(y0))))))) MARK(hd(incr(adx(hd(hd(incr(y0))))))) -> c16(MARK(incr(adx(hd(hd(incr(y0))))))) MARK(hd(incr(adx(hd(hd(hd(y0))))))) -> c16(MARK(incr(adx(hd(hd(hd(y0))))))) MARK(hd(incr(adx(hd(hd(tl(y0))))))) -> c16(MARK(incr(adx(hd(hd(tl(y0))))))) MARK(hd(incr(adx(hd(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(hd(cons(y0, y1))))))) MARK(hd(incr(adx(hd(hd(y0)))))) -> c16(MARK(incr(adx(hd(hd(y0)))))) MARK(hd(incr(adx(hd(tl(nats)))))) -> c16(MARK(incr(adx(hd(tl(nats)))))) MARK(hd(incr(adx(hd(tl(adx(y0))))))) -> c16(MARK(incr(adx(hd(tl(adx(y0))))))) MARK(hd(incr(adx(hd(tl(incr(y0))))))) -> c16(MARK(incr(adx(hd(tl(incr(y0))))))) MARK(hd(incr(adx(hd(tl(hd(y0))))))) -> c16(MARK(incr(adx(hd(tl(hd(y0))))))) MARK(hd(incr(adx(hd(tl(tl(y0))))))) -> c16(MARK(incr(adx(hd(tl(tl(y0))))))) MARK(hd(incr(adx(hd(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(tl(cons(y0, y1))))))) MARK(hd(incr(adx(hd(tl(y0)))))) -> c16(MARK(incr(adx(hd(tl(y0)))))) MARK(hd(incr(adx(hd(nats))))) -> c16(MARK(incr(adx(hd(nats))))) MARK(hd(incr(adx(tl(adx(nats)))))) -> c16(MARK(incr(adx(tl(adx(nats)))))) MARK(hd(incr(adx(tl(adx(adx(y0))))))) -> c16(MARK(incr(adx(tl(adx(adx(y0))))))) MARK(hd(incr(adx(tl(adx(zeros)))))) -> c16(MARK(incr(adx(tl(adx(zeros)))))) MARK(hd(incr(adx(tl(adx(incr(y0))))))) -> c16(MARK(incr(adx(tl(adx(incr(y0))))))) MARK(hd(incr(adx(tl(adx(hd(y0))))))) -> c16(MARK(incr(adx(tl(adx(hd(y0))))))) MARK(hd(incr(adx(tl(adx(tl(y0))))))) -> c16(MARK(incr(adx(tl(adx(tl(y0))))))) MARK(hd(incr(adx(tl(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(adx(cons(y0, y1))))))) MARK(hd(incr(adx(tl(adx(y0)))))) -> c16(MARK(incr(adx(tl(adx(y0)))))) MARK(hd(incr(adx(tl(incr(nats)))))) -> c16(MARK(incr(adx(tl(incr(nats)))))) MARK(hd(incr(adx(tl(incr(adx(y0))))))) -> c16(MARK(incr(adx(tl(incr(adx(y0))))))) MARK(hd(incr(adx(tl(incr(zeros)))))) -> c16(MARK(incr(adx(tl(incr(zeros)))))) MARK(hd(incr(adx(tl(incr(incr(y0))))))) -> c16(MARK(incr(adx(tl(incr(incr(y0))))))) MARK(hd(incr(adx(tl(incr(hd(y0))))))) -> c16(MARK(incr(adx(tl(incr(hd(y0))))))) MARK(hd(incr(adx(tl(incr(tl(y0))))))) -> c16(MARK(incr(adx(tl(incr(tl(y0))))))) MARK(hd(incr(adx(tl(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(incr(cons(y0, y1))))))) MARK(hd(incr(adx(tl(incr(s(y0))))))) -> c16(MARK(incr(adx(tl(incr(s(y0))))))) MARK(hd(incr(adx(tl(incr(y0)))))) -> c16(MARK(incr(adx(tl(incr(y0)))))) MARK(hd(incr(adx(tl(hd(nats)))))) -> c16(MARK(incr(adx(tl(hd(nats)))))) MARK(hd(incr(adx(tl(hd(adx(y0))))))) -> c16(MARK(incr(adx(tl(hd(adx(y0))))))) MARK(hd(incr(adx(tl(hd(incr(y0))))))) -> c16(MARK(incr(adx(tl(hd(incr(y0))))))) MARK(hd(incr(adx(tl(hd(hd(y0))))))) -> c16(MARK(incr(adx(tl(hd(hd(y0))))))) MARK(hd(incr(adx(tl(hd(tl(y0))))))) -> c16(MARK(incr(adx(tl(hd(tl(y0))))))) MARK(hd(incr(adx(tl(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(hd(cons(y0, y1))))))) MARK(hd(incr(adx(tl(hd(y0)))))) -> c16(MARK(incr(adx(tl(hd(y0)))))) MARK(hd(incr(adx(tl(tl(nats)))))) -> c16(MARK(incr(adx(tl(tl(nats)))))) MARK(hd(incr(adx(tl(tl(adx(y0))))))) -> c16(MARK(incr(adx(tl(tl(adx(y0))))))) MARK(hd(incr(adx(tl(tl(incr(y0))))))) -> c16(MARK(incr(adx(tl(tl(incr(y0))))))) MARK(hd(incr(adx(tl(tl(hd(y0))))))) -> c16(MARK(incr(adx(tl(tl(hd(y0))))))) MARK(hd(incr(adx(tl(tl(tl(y0))))))) -> c16(MARK(incr(adx(tl(tl(tl(y0))))))) MARK(hd(incr(adx(tl(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(tl(cons(y0, y1))))))) MARK(hd(incr(adx(tl(tl(y0)))))) -> c16(MARK(incr(adx(tl(tl(y0)))))) MARK(hd(incr(adx(tl(nats))))) -> c16(MARK(incr(adx(tl(nats))))) MARK(hd(incr(adx(hd(adx(0)))))) -> c16(MARK(incr(adx(hd(adx(0)))))) MARK(hd(incr(adx(hd(adx(s(y0))))))) -> c16(MARK(incr(adx(hd(adx(s(y0))))))) MARK(hd(incr(adx(hd(incr(0)))))) -> c16(MARK(incr(adx(hd(incr(0)))))) MARK(hd(incr(adx(hd(incr(s(y0))))))) -> c16(MARK(incr(adx(hd(incr(s(y0))))))) MARK(hd(incr(adx(hd(hd(zeros)))))) -> c16(MARK(incr(adx(hd(hd(zeros)))))) MARK(hd(incr(adx(tl(hd(zeros)))))) -> c16(MARK(incr(adx(tl(hd(zeros)))))) MARK(hd(incr(adx(tl(adx(0)))))) -> c16(MARK(incr(adx(tl(adx(0)))))) MARK(hd(incr(adx(hd(tl(zeros)))))) -> c16(MARK(incr(adx(hd(tl(zeros)))))) MARK(hd(incr(adx(tl(tl(zeros)))))) -> c16(MARK(incr(adx(tl(tl(zeros)))))) MARK(hd(incr(adx(tl(adx(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) MARK(hd(incr(adx(tl(incr(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) MARK(hd(incr(hd(adx(nats))))) -> c16(MARK(incr(hd(adx(nats))))) MARK(hd(incr(hd(adx(zeros))))) -> c16(MARK(incr(hd(adx(zeros))))) MARK(hd(incr(hd(adx(cons(y0, y1)))))) -> c16(MARK(incr(hd(adx(cons(y0, y1)))))) MARK(hd(incr(tl(adx(nats))))) -> c16(MARK(incr(tl(adx(nats))))) MARK(hd(incr(tl(adx(zeros))))) -> c16(MARK(incr(tl(adx(zeros))))) MARK(hd(incr(tl(adx(cons(y0, y1)))))) -> c16(MARK(incr(tl(adx(cons(y0, y1)))))) MARK(hd(incr(tl(incr(s(y0)))))) -> c16(MARK(incr(tl(incr(s(y0)))))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c16_2, c16_1, c17_2, c17_1, c8_1, c10_1, c13_1, c15_1 ---------------------------------------- (211) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) MARK(tl(cons(z0, adx(y1)))) -> c17(A__TL(cons(z0, adx(y1)))) MARK(tl(cons(z0, incr(y1)))) -> c17(A__TL(cons(z0, incr(y1)))) MARK(tl(cons(z0, hd(cons(y1, y2))))) -> c17(A__TL(cons(z0, hd(cons(y1, y2))))) MARK(tl(cons(z0, tl(cons(y1, y2))))) -> c17(A__TL(cons(z0, tl(cons(y1, y2))))) MARK(tl(cons(z0, hd(adx(nats))))) -> c17(A__TL(cons(z0, hd(adx(nats))))) MARK(tl(cons(z0, hd(adx(adx(y1)))))) -> c17(A__TL(cons(z0, hd(adx(adx(y1)))))) MARK(tl(cons(z0, hd(adx(zeros))))) -> c17(A__TL(cons(z0, hd(adx(zeros))))) MARK(tl(cons(z0, hd(adx(incr(y1)))))) -> c17(A__TL(cons(z0, hd(adx(incr(y1)))))) MARK(tl(cons(z0, hd(adx(hd(y1)))))) -> c17(A__TL(cons(z0, hd(adx(hd(y1)))))) MARK(tl(cons(z0, hd(adx(tl(y1)))))) -> c17(A__TL(cons(z0, hd(adx(tl(y1)))))) MARK(tl(cons(z0, hd(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(adx(cons(y1, y2)))))) MARK(tl(cons(z0, hd(adx(y1))))) -> c17(A__TL(cons(z0, hd(adx(y1))))) MARK(tl(cons(z0, hd(incr(nats))))) -> c17(A__TL(cons(z0, hd(incr(nats))))) MARK(tl(cons(z0, hd(incr(adx(y1)))))) -> c17(A__TL(cons(z0, hd(incr(adx(y1)))))) MARK(tl(cons(z0, hd(incr(zeros))))) -> c17(A__TL(cons(z0, hd(incr(zeros))))) MARK(tl(cons(z0, hd(incr(incr(y1)))))) -> c17(A__TL(cons(z0, hd(incr(incr(y1)))))) MARK(tl(cons(z0, hd(incr(hd(y1)))))) -> c17(A__TL(cons(z0, hd(incr(hd(y1)))))) MARK(tl(cons(z0, hd(incr(tl(y1)))))) -> c17(A__TL(cons(z0, hd(incr(tl(y1)))))) MARK(tl(cons(z0, hd(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(incr(cons(y1, y2)))))) MARK(tl(cons(z0, hd(incr(y1))))) -> c17(A__TL(cons(z0, hd(incr(y1))))) MARK(tl(cons(z0, hd(hd(nats))))) -> c17(A__TL(cons(z0, hd(hd(nats))))) MARK(tl(cons(z0, hd(hd(adx(y1)))))) -> c17(A__TL(cons(z0, hd(hd(adx(y1)))))) MARK(tl(cons(z0, hd(hd(incr(y1)))))) -> c17(A__TL(cons(z0, hd(hd(incr(y1)))))) MARK(tl(cons(z0, hd(hd(hd(y1)))))) -> c17(A__TL(cons(z0, hd(hd(hd(y1)))))) MARK(tl(cons(z0, hd(hd(tl(y1)))))) -> c17(A__TL(cons(z0, hd(hd(tl(y1)))))) MARK(tl(cons(z0, hd(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(hd(cons(y1, y2)))))) MARK(tl(cons(z0, hd(hd(y1))))) -> c17(A__TL(cons(z0, hd(hd(y1))))) MARK(tl(cons(z0, hd(tl(nats))))) -> c17(A__TL(cons(z0, hd(tl(nats))))) MARK(tl(cons(z0, hd(tl(adx(y1)))))) -> c17(A__TL(cons(z0, hd(tl(adx(y1)))))) MARK(tl(cons(z0, hd(tl(zeros))))) -> c17(A__TL(cons(z0, hd(tl(zeros))))) MARK(tl(cons(z0, hd(tl(incr(y1)))))) -> c17(A__TL(cons(z0, hd(tl(incr(y1)))))) MARK(tl(cons(z0, hd(tl(hd(y1)))))) -> c17(A__TL(cons(z0, hd(tl(hd(y1)))))) MARK(tl(cons(z0, hd(tl(tl(y1)))))) -> c17(A__TL(cons(z0, hd(tl(tl(y1)))))) MARK(tl(cons(z0, hd(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(tl(cons(y1, y2)))))) MARK(tl(cons(z0, hd(tl(y1))))) -> c17(A__TL(cons(z0, hd(tl(y1))))) MARK(tl(cons(z0, hd(nats)))) -> c17(A__TL(cons(z0, hd(nats)))) MARK(tl(cons(z0, tl(adx(nats))))) -> c17(A__TL(cons(z0, tl(adx(nats))))) MARK(tl(cons(z0, tl(adx(adx(y1)))))) -> c17(A__TL(cons(z0, tl(adx(adx(y1)))))) MARK(tl(cons(z0, tl(adx(zeros))))) -> c17(A__TL(cons(z0, tl(adx(zeros))))) MARK(tl(cons(z0, tl(adx(incr(y1)))))) -> c17(A__TL(cons(z0, tl(adx(incr(y1)))))) MARK(tl(cons(z0, tl(adx(hd(y1)))))) -> c17(A__TL(cons(z0, tl(adx(hd(y1)))))) MARK(tl(cons(z0, tl(adx(tl(y1)))))) -> c17(A__TL(cons(z0, tl(adx(tl(y1)))))) MARK(tl(cons(z0, tl(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(adx(cons(y1, y2)))))) MARK(tl(cons(z0, tl(adx(s(y1)))))) -> c17(A__TL(cons(z0, tl(adx(s(y1)))))) MARK(tl(cons(z0, tl(adx(y1))))) -> c17(A__TL(cons(z0, tl(adx(y1))))) MARK(tl(cons(z0, tl(incr(nats))))) -> c17(A__TL(cons(z0, tl(incr(nats))))) MARK(tl(cons(z0, tl(incr(adx(y1)))))) -> c17(A__TL(cons(z0, tl(incr(adx(y1)))))) MARK(tl(cons(z0, tl(incr(zeros))))) -> c17(A__TL(cons(z0, tl(incr(zeros))))) MARK(tl(cons(z0, tl(incr(incr(y1)))))) -> c17(A__TL(cons(z0, tl(incr(incr(y1)))))) MARK(tl(cons(z0, tl(incr(hd(y1)))))) -> c17(A__TL(cons(z0, tl(incr(hd(y1)))))) MARK(tl(cons(z0, tl(incr(tl(y1)))))) -> c17(A__TL(cons(z0, tl(incr(tl(y1)))))) MARK(tl(cons(z0, tl(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(incr(cons(y1, y2)))))) MARK(tl(cons(z0, tl(incr(0))))) -> c17(A__TL(cons(z0, tl(incr(0))))) MARK(tl(cons(z0, tl(incr(s(y1)))))) -> c17(A__TL(cons(z0, tl(incr(s(y1)))))) MARK(tl(cons(z0, tl(incr(y1))))) -> c17(A__TL(cons(z0, tl(incr(y1))))) MARK(tl(cons(z0, tl(hd(nats))))) -> c17(A__TL(cons(z0, tl(hd(nats))))) MARK(tl(cons(z0, tl(hd(adx(y1)))))) -> c17(A__TL(cons(z0, tl(hd(adx(y1)))))) MARK(tl(cons(z0, tl(hd(incr(y1)))))) -> c17(A__TL(cons(z0, tl(hd(incr(y1)))))) MARK(tl(cons(z0, tl(hd(hd(y1)))))) -> c17(A__TL(cons(z0, tl(hd(hd(y1)))))) MARK(tl(cons(z0, tl(hd(tl(y1)))))) -> c17(A__TL(cons(z0, tl(hd(tl(y1)))))) MARK(tl(cons(z0, tl(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(hd(cons(y1, y2)))))) MARK(tl(cons(z0, tl(hd(y1))))) -> c17(A__TL(cons(z0, tl(hd(y1))))) MARK(tl(cons(z0, tl(tl(nats))))) -> c17(A__TL(cons(z0, tl(tl(nats))))) MARK(tl(cons(z0, tl(tl(adx(y1)))))) -> c17(A__TL(cons(z0, tl(tl(adx(y1)))))) MARK(tl(cons(z0, tl(tl(zeros))))) -> c17(A__TL(cons(z0, tl(tl(zeros))))) MARK(tl(cons(z0, tl(tl(incr(y1)))))) -> c17(A__TL(cons(z0, tl(tl(incr(y1)))))) MARK(tl(cons(z0, tl(tl(hd(y1)))))) -> c17(A__TL(cons(z0, tl(tl(hd(y1)))))) MARK(tl(cons(z0, tl(tl(tl(y1)))))) -> c17(A__TL(cons(z0, tl(tl(tl(y1)))))) MARK(tl(cons(z0, tl(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(tl(cons(y1, y2)))))) MARK(tl(cons(z0, tl(tl(y1))))) -> c17(A__TL(cons(z0, tl(tl(y1))))) MARK(tl(cons(z0, tl(nats)))) -> c17(A__TL(cons(z0, tl(nats)))) MARK(tl(cons(z0, hd(adx(0))))) -> c17(A__TL(cons(z0, hd(adx(0))))) MARK(tl(cons(z0, hd(adx(s(y1)))))) -> c17(A__TL(cons(z0, hd(adx(s(y1)))))) MARK(tl(cons(z0, hd(incr(0))))) -> c17(A__TL(cons(z0, hd(incr(0))))) MARK(tl(cons(z0, hd(incr(s(y1)))))) -> c17(A__TL(cons(z0, hd(incr(s(y1)))))) MARK(tl(cons(z0, hd(hd(zeros))))) -> c17(A__TL(cons(z0, hd(hd(zeros))))) MARK(tl(cons(z0, tl(hd(zeros))))) -> c17(A__TL(cons(z0, tl(hd(zeros))))) MARK(tl(cons(z0, tl(adx(0))))) -> c17(A__TL(cons(z0, tl(adx(0))))) MARK(hd(adx(adx(y0)))) -> c16(MARK(adx(adx(y0)))) MARK(hd(adx(incr(y0)))) -> c16(MARK(adx(incr(y0)))) MARK(hd(adx(hd(cons(y0, y1))))) -> c16(MARK(adx(hd(cons(y0, y1))))) MARK(hd(adx(tl(cons(y0, y1))))) -> c16(MARK(adx(tl(cons(y0, y1))))) MARK(hd(adx(hd(adx(nats))))) -> c16(MARK(adx(hd(adx(nats))))) MARK(hd(adx(hd(adx(adx(y0)))))) -> c16(MARK(adx(hd(adx(adx(y0)))))) MARK(hd(adx(hd(adx(zeros))))) -> c16(MARK(adx(hd(adx(zeros))))) MARK(hd(adx(hd(adx(incr(y0)))))) -> c16(MARK(adx(hd(adx(incr(y0)))))) MARK(hd(adx(hd(adx(hd(y0)))))) -> c16(MARK(adx(hd(adx(hd(y0)))))) MARK(hd(adx(hd(adx(tl(y0)))))) -> c16(MARK(adx(hd(adx(tl(y0)))))) MARK(hd(adx(hd(adx(cons(y0, y1)))))) -> c16(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(hd(adx(hd(adx(y0))))) -> c16(MARK(adx(hd(adx(y0))))) MARK(hd(adx(hd(incr(nats))))) -> c16(MARK(adx(hd(incr(nats))))) MARK(hd(adx(hd(incr(adx(y0)))))) -> c16(MARK(adx(hd(incr(adx(y0)))))) MARK(hd(adx(hd(incr(zeros))))) -> c16(MARK(adx(hd(incr(zeros))))) MARK(hd(adx(hd(incr(incr(y0)))))) -> c16(MARK(adx(hd(incr(incr(y0)))))) MARK(hd(adx(hd(incr(hd(y0)))))) -> c16(MARK(adx(hd(incr(hd(y0)))))) MARK(hd(adx(hd(incr(tl(y0)))))) -> c16(MARK(adx(hd(incr(tl(y0)))))) MARK(hd(adx(hd(incr(cons(y0, y1)))))) -> c16(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(hd(adx(hd(incr(y0))))) -> c16(MARK(adx(hd(incr(y0))))) MARK(hd(adx(hd(hd(nats))))) -> c16(MARK(adx(hd(hd(nats))))) MARK(hd(adx(hd(hd(adx(y0)))))) -> c16(MARK(adx(hd(hd(adx(y0)))))) MARK(hd(adx(hd(hd(incr(y0)))))) -> c16(MARK(adx(hd(hd(incr(y0)))))) MARK(hd(adx(hd(hd(hd(y0)))))) -> c16(MARK(adx(hd(hd(hd(y0)))))) MARK(hd(adx(hd(hd(tl(y0)))))) -> c16(MARK(adx(hd(hd(tl(y0)))))) MARK(hd(adx(hd(hd(cons(y0, y1)))))) -> c16(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(hd(adx(hd(hd(y0))))) -> c16(MARK(adx(hd(hd(y0))))) MARK(hd(adx(hd(tl(nats))))) -> c16(MARK(adx(hd(tl(nats))))) MARK(hd(adx(hd(tl(adx(y0)))))) -> c16(MARK(adx(hd(tl(adx(y0)))))) MARK(hd(adx(hd(tl(incr(y0)))))) -> c16(MARK(adx(hd(tl(incr(y0)))))) MARK(hd(adx(hd(tl(hd(y0)))))) -> c16(MARK(adx(hd(tl(hd(y0)))))) MARK(hd(adx(hd(tl(tl(y0)))))) -> c16(MARK(adx(hd(tl(tl(y0)))))) MARK(hd(adx(hd(tl(cons(y0, y1)))))) -> c16(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(hd(adx(hd(tl(y0))))) -> c16(MARK(adx(hd(tl(y0))))) MARK(hd(adx(hd(nats)))) -> c16(MARK(adx(hd(nats)))) MARK(hd(adx(tl(adx(nats))))) -> c16(MARK(adx(tl(adx(nats))))) MARK(hd(adx(tl(adx(adx(y0)))))) -> c16(MARK(adx(tl(adx(adx(y0)))))) MARK(hd(adx(tl(adx(zeros))))) -> c16(MARK(adx(tl(adx(zeros))))) MARK(hd(adx(tl(adx(incr(y0)))))) -> c16(MARK(adx(tl(adx(incr(y0)))))) MARK(hd(adx(tl(adx(hd(y0)))))) -> c16(MARK(adx(tl(adx(hd(y0)))))) MARK(hd(adx(tl(adx(tl(y0)))))) -> c16(MARK(adx(tl(adx(tl(y0)))))) MARK(hd(adx(tl(adx(cons(y0, y1)))))) -> c16(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(hd(adx(tl(adx(y0))))) -> c16(MARK(adx(tl(adx(y0))))) MARK(hd(adx(tl(incr(nats))))) -> c16(MARK(adx(tl(incr(nats))))) MARK(hd(adx(tl(incr(adx(y0)))))) -> c16(MARK(adx(tl(incr(adx(y0)))))) MARK(hd(adx(tl(incr(zeros))))) -> c16(MARK(adx(tl(incr(zeros))))) MARK(hd(adx(tl(incr(incr(y0)))))) -> c16(MARK(adx(tl(incr(incr(y0)))))) MARK(hd(adx(tl(incr(hd(y0)))))) -> c16(MARK(adx(tl(incr(hd(y0)))))) MARK(hd(adx(tl(incr(tl(y0)))))) -> c16(MARK(adx(tl(incr(tl(y0)))))) MARK(hd(adx(tl(incr(cons(y0, y1)))))) -> c16(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(hd(adx(tl(incr(s(y0)))))) -> c16(MARK(adx(tl(incr(s(y0)))))) MARK(hd(adx(tl(incr(y0))))) -> c16(MARK(adx(tl(incr(y0))))) MARK(hd(adx(tl(hd(nats))))) -> c16(MARK(adx(tl(hd(nats))))) MARK(hd(adx(tl(hd(adx(y0)))))) -> c16(MARK(adx(tl(hd(adx(y0)))))) MARK(hd(adx(tl(hd(incr(y0)))))) -> c16(MARK(adx(tl(hd(incr(y0)))))) MARK(hd(adx(tl(hd(hd(y0)))))) -> c16(MARK(adx(tl(hd(hd(y0)))))) MARK(hd(adx(tl(hd(tl(y0)))))) -> c16(MARK(adx(tl(hd(tl(y0)))))) MARK(hd(adx(tl(hd(cons(y0, y1)))))) -> c16(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(hd(adx(tl(hd(y0))))) -> c16(MARK(adx(tl(hd(y0))))) MARK(hd(adx(tl(tl(nats))))) -> c16(MARK(adx(tl(tl(nats))))) MARK(hd(adx(tl(tl(adx(y0)))))) -> c16(MARK(adx(tl(tl(adx(y0)))))) MARK(hd(adx(tl(tl(incr(y0)))))) -> c16(MARK(adx(tl(tl(incr(y0)))))) MARK(hd(adx(tl(tl(hd(y0)))))) -> c16(MARK(adx(tl(tl(hd(y0)))))) MARK(hd(adx(tl(tl(tl(y0)))))) -> c16(MARK(adx(tl(tl(tl(y0)))))) MARK(hd(adx(tl(tl(cons(y0, y1)))))) -> c16(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(hd(adx(tl(tl(y0))))) -> c16(MARK(adx(tl(tl(y0))))) MARK(hd(adx(tl(nats)))) -> c16(MARK(adx(tl(nats)))) MARK(hd(adx(hd(adx(0))))) -> c16(MARK(adx(hd(adx(0))))) MARK(hd(adx(hd(adx(s(y0)))))) -> c16(MARK(adx(hd(adx(s(y0)))))) MARK(hd(adx(hd(incr(0))))) -> c16(MARK(adx(hd(incr(0))))) MARK(hd(adx(hd(incr(s(y0)))))) -> c16(MARK(adx(hd(incr(s(y0)))))) MARK(hd(adx(hd(hd(zeros))))) -> c16(MARK(adx(hd(hd(zeros))))) MARK(hd(adx(tl(hd(zeros))))) -> c16(MARK(adx(tl(hd(zeros))))) MARK(hd(adx(tl(adx(0))))) -> c16(MARK(adx(tl(adx(0))))) MARK(hd(adx(hd(tl(zeros))))) -> c16(MARK(adx(hd(tl(zeros))))) MARK(hd(adx(tl(tl(zeros))))) -> c16(MARK(adx(tl(tl(zeros))))) MARK(hd(adx(tl(adx(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) MARK(hd(adx(tl(incr(0))))) -> c16(MARK(adx(tl(incr(0))))) MARK(hd(incr(incr(y0)))) -> c16(MARK(incr(incr(y0)))) MARK(hd(incr(hd(cons(y0, y1))))) -> c16(MARK(incr(hd(cons(y0, y1))))) MARK(hd(incr(tl(cons(y0, y1))))) -> c16(MARK(incr(tl(cons(y0, y1))))) MARK(hd(incr(hd(adx(adx(y0)))))) -> c16(MARK(incr(hd(adx(adx(y0)))))) MARK(hd(incr(hd(adx(incr(y0)))))) -> c16(MARK(incr(hd(adx(incr(y0)))))) MARK(hd(incr(hd(adx(hd(y0)))))) -> c16(MARK(incr(hd(adx(hd(y0)))))) MARK(hd(incr(hd(adx(tl(y0)))))) -> c16(MARK(incr(hd(adx(tl(y0)))))) MARK(hd(incr(hd(adx(y0))))) -> c16(MARK(incr(hd(adx(y0))))) MARK(hd(incr(hd(incr(nats))))) -> c16(MARK(incr(hd(incr(nats))))) MARK(hd(incr(hd(incr(adx(y0)))))) -> c16(MARK(incr(hd(incr(adx(y0)))))) MARK(hd(incr(hd(incr(zeros))))) -> c16(MARK(incr(hd(incr(zeros))))) MARK(hd(incr(hd(incr(incr(y0)))))) -> c16(MARK(incr(hd(incr(incr(y0)))))) MARK(hd(incr(hd(incr(hd(y0)))))) -> c16(MARK(incr(hd(incr(hd(y0)))))) MARK(hd(incr(hd(incr(tl(y0)))))) -> c16(MARK(incr(hd(incr(tl(y0)))))) MARK(hd(incr(hd(incr(cons(y0, y1)))))) -> c16(MARK(incr(hd(incr(cons(y0, y1)))))) MARK(hd(incr(hd(incr(y0))))) -> c16(MARK(incr(hd(incr(y0))))) MARK(hd(incr(hd(hd(nats))))) -> c16(MARK(incr(hd(hd(nats))))) MARK(hd(incr(hd(hd(adx(y0)))))) -> c16(MARK(incr(hd(hd(adx(y0)))))) MARK(hd(incr(hd(hd(incr(y0)))))) -> c16(MARK(incr(hd(hd(incr(y0)))))) MARK(hd(incr(hd(hd(hd(y0)))))) -> c16(MARK(incr(hd(hd(hd(y0)))))) MARK(hd(incr(hd(hd(tl(y0)))))) -> c16(MARK(incr(hd(hd(tl(y0)))))) MARK(hd(incr(hd(hd(cons(y0, y1)))))) -> c16(MARK(incr(hd(hd(cons(y0, y1)))))) MARK(hd(incr(hd(hd(y0))))) -> c16(MARK(incr(hd(hd(y0))))) MARK(hd(incr(hd(tl(nats))))) -> c16(MARK(incr(hd(tl(nats))))) MARK(hd(incr(hd(tl(adx(y0)))))) -> c16(MARK(incr(hd(tl(adx(y0)))))) MARK(hd(incr(hd(tl(incr(y0)))))) -> c16(MARK(incr(hd(tl(incr(y0)))))) MARK(hd(incr(hd(tl(hd(y0)))))) -> c16(MARK(incr(hd(tl(hd(y0)))))) MARK(hd(incr(hd(tl(tl(y0)))))) -> c16(MARK(incr(hd(tl(tl(y0)))))) MARK(hd(incr(hd(tl(cons(y0, y1)))))) -> c16(MARK(incr(hd(tl(cons(y0, y1)))))) MARK(hd(incr(hd(tl(y0))))) -> c16(MARK(incr(hd(tl(y0))))) MARK(hd(incr(hd(nats)))) -> c16(MARK(incr(hd(nats)))) MARK(hd(incr(tl(adx(adx(y0)))))) -> c16(MARK(incr(tl(adx(adx(y0)))))) MARK(hd(incr(tl(adx(incr(y0)))))) -> c16(MARK(incr(tl(adx(incr(y0)))))) MARK(hd(incr(tl(adx(hd(y0)))))) -> c16(MARK(incr(tl(adx(hd(y0)))))) MARK(hd(incr(tl(adx(tl(y0)))))) -> c16(MARK(incr(tl(adx(tl(y0)))))) MARK(hd(incr(tl(adx(y0))))) -> c16(MARK(incr(tl(adx(y0))))) MARK(hd(incr(tl(incr(nats))))) -> c16(MARK(incr(tl(incr(nats))))) MARK(hd(incr(tl(incr(adx(y0)))))) -> c16(MARK(incr(tl(incr(adx(y0)))))) MARK(hd(incr(tl(incr(zeros))))) -> c16(MARK(incr(tl(incr(zeros))))) MARK(hd(incr(tl(incr(incr(y0)))))) -> c16(MARK(incr(tl(incr(incr(y0)))))) MARK(hd(incr(tl(incr(hd(y0)))))) -> c16(MARK(incr(tl(incr(hd(y0)))))) MARK(hd(incr(tl(incr(tl(y0)))))) -> c16(MARK(incr(tl(incr(tl(y0)))))) MARK(hd(incr(tl(incr(cons(y0, y1)))))) -> c16(MARK(incr(tl(incr(cons(y0, y1)))))) MARK(hd(incr(tl(incr(y0))))) -> c16(MARK(incr(tl(incr(y0))))) MARK(hd(incr(tl(hd(nats))))) -> c16(MARK(incr(tl(hd(nats))))) MARK(hd(incr(tl(hd(adx(y0)))))) -> c16(MARK(incr(tl(hd(adx(y0)))))) MARK(hd(incr(tl(hd(incr(y0)))))) -> c16(MARK(incr(tl(hd(incr(y0)))))) MARK(hd(incr(tl(hd(hd(y0)))))) -> c16(MARK(incr(tl(hd(hd(y0)))))) MARK(hd(incr(tl(hd(tl(y0)))))) -> c16(MARK(incr(tl(hd(tl(y0)))))) MARK(hd(incr(tl(hd(cons(y0, y1)))))) -> c16(MARK(incr(tl(hd(cons(y0, y1)))))) MARK(hd(incr(tl(hd(y0))))) -> c16(MARK(incr(tl(hd(y0))))) MARK(hd(incr(tl(tl(nats))))) -> c16(MARK(incr(tl(tl(nats))))) MARK(hd(incr(tl(tl(adx(y0)))))) -> c16(MARK(incr(tl(tl(adx(y0)))))) MARK(hd(incr(tl(tl(incr(y0)))))) -> c16(MARK(incr(tl(tl(incr(y0)))))) MARK(hd(incr(tl(tl(hd(y0)))))) -> c16(MARK(incr(tl(tl(hd(y0)))))) MARK(hd(incr(tl(tl(tl(y0)))))) -> c16(MARK(incr(tl(tl(tl(y0)))))) MARK(hd(incr(tl(tl(cons(y0, y1)))))) -> c16(MARK(incr(tl(tl(cons(y0, y1)))))) MARK(hd(incr(tl(tl(y0))))) -> c16(MARK(incr(tl(tl(y0))))) MARK(hd(incr(tl(nats)))) -> c16(MARK(incr(tl(nats)))) MARK(hd(incr(hd(incr(0))))) -> c16(MARK(incr(hd(incr(0))))) MARK(hd(incr(hd(incr(s(y0)))))) -> c16(MARK(incr(hd(incr(s(y0)))))) MARK(hd(incr(hd(hd(zeros))))) -> c16(MARK(incr(hd(hd(zeros))))) MARK(hd(incr(tl(hd(zeros))))) -> c16(MARK(incr(tl(hd(zeros))))) MARK(hd(incr(hd(tl(zeros))))) -> c16(MARK(incr(hd(tl(zeros))))) MARK(hd(incr(tl(tl(zeros))))) -> c16(MARK(incr(tl(tl(zeros))))) MARK(hd(incr(tl(incr(0))))) -> c16(MARK(incr(tl(incr(0))))) MARK(hd(incr(adx(adx(y0))))) -> c16(MARK(incr(adx(adx(y0))))) MARK(hd(incr(adx(incr(y0))))) -> c16(MARK(incr(adx(incr(y0))))) MARK(hd(incr(adx(hd(cons(y0, y1)))))) -> c16(MARK(incr(adx(hd(cons(y0, y1)))))) MARK(hd(incr(adx(tl(cons(y0, y1)))))) -> c16(MARK(incr(adx(tl(cons(y0, y1)))))) MARK(hd(incr(adx(hd(adx(nats)))))) -> c16(MARK(incr(adx(hd(adx(nats)))))) MARK(hd(incr(adx(hd(adx(adx(y0))))))) -> c16(MARK(incr(adx(hd(adx(adx(y0))))))) MARK(hd(incr(adx(hd(adx(zeros)))))) -> c16(MARK(incr(adx(hd(adx(zeros)))))) MARK(hd(incr(adx(hd(adx(incr(y0))))))) -> c16(MARK(incr(adx(hd(adx(incr(y0))))))) MARK(hd(incr(adx(hd(adx(hd(y0))))))) -> c16(MARK(incr(adx(hd(adx(hd(y0))))))) MARK(hd(incr(adx(hd(adx(tl(y0))))))) -> c16(MARK(incr(adx(hd(adx(tl(y0))))))) MARK(hd(incr(adx(hd(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(adx(cons(y0, y1))))))) MARK(hd(incr(adx(hd(adx(y0)))))) -> c16(MARK(incr(adx(hd(adx(y0)))))) MARK(hd(incr(adx(hd(incr(nats)))))) -> c16(MARK(incr(adx(hd(incr(nats)))))) MARK(hd(incr(adx(hd(incr(adx(y0))))))) -> c16(MARK(incr(adx(hd(incr(adx(y0))))))) MARK(hd(incr(adx(hd(incr(zeros)))))) -> c16(MARK(incr(adx(hd(incr(zeros)))))) MARK(hd(incr(adx(hd(incr(incr(y0))))))) -> c16(MARK(incr(adx(hd(incr(incr(y0))))))) MARK(hd(incr(adx(hd(incr(hd(y0))))))) -> c16(MARK(incr(adx(hd(incr(hd(y0))))))) MARK(hd(incr(adx(hd(incr(tl(y0))))))) -> c16(MARK(incr(adx(hd(incr(tl(y0))))))) MARK(hd(incr(adx(hd(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(incr(cons(y0, y1))))))) MARK(hd(incr(adx(hd(incr(y0)))))) -> c16(MARK(incr(adx(hd(incr(y0)))))) MARK(hd(incr(adx(hd(hd(nats)))))) -> c16(MARK(incr(adx(hd(hd(nats)))))) MARK(hd(incr(adx(hd(hd(adx(y0))))))) -> c16(MARK(incr(adx(hd(hd(adx(y0))))))) MARK(hd(incr(adx(hd(hd(incr(y0))))))) -> c16(MARK(incr(adx(hd(hd(incr(y0))))))) MARK(hd(incr(adx(hd(hd(hd(y0))))))) -> c16(MARK(incr(adx(hd(hd(hd(y0))))))) MARK(hd(incr(adx(hd(hd(tl(y0))))))) -> c16(MARK(incr(adx(hd(hd(tl(y0))))))) MARK(hd(incr(adx(hd(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(hd(cons(y0, y1))))))) MARK(hd(incr(adx(hd(hd(y0)))))) -> c16(MARK(incr(adx(hd(hd(y0)))))) MARK(hd(incr(adx(hd(tl(nats)))))) -> c16(MARK(incr(adx(hd(tl(nats)))))) MARK(hd(incr(adx(hd(tl(adx(y0))))))) -> c16(MARK(incr(adx(hd(tl(adx(y0))))))) MARK(hd(incr(adx(hd(tl(incr(y0))))))) -> c16(MARK(incr(adx(hd(tl(incr(y0))))))) MARK(hd(incr(adx(hd(tl(hd(y0))))))) -> c16(MARK(incr(adx(hd(tl(hd(y0))))))) MARK(hd(incr(adx(hd(tl(tl(y0))))))) -> c16(MARK(incr(adx(hd(tl(tl(y0))))))) MARK(hd(incr(adx(hd(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(tl(cons(y0, y1))))))) MARK(hd(incr(adx(hd(tl(y0)))))) -> c16(MARK(incr(adx(hd(tl(y0)))))) MARK(hd(incr(adx(hd(nats))))) -> c16(MARK(incr(adx(hd(nats))))) MARK(hd(incr(adx(tl(adx(nats)))))) -> c16(MARK(incr(adx(tl(adx(nats)))))) MARK(hd(incr(adx(tl(adx(adx(y0))))))) -> c16(MARK(incr(adx(tl(adx(adx(y0))))))) MARK(hd(incr(adx(tl(adx(zeros)))))) -> c16(MARK(incr(adx(tl(adx(zeros)))))) MARK(hd(incr(adx(tl(adx(incr(y0))))))) -> c16(MARK(incr(adx(tl(adx(incr(y0))))))) MARK(hd(incr(adx(tl(adx(hd(y0))))))) -> c16(MARK(incr(adx(tl(adx(hd(y0))))))) MARK(hd(incr(adx(tl(adx(tl(y0))))))) -> c16(MARK(incr(adx(tl(adx(tl(y0))))))) MARK(hd(incr(adx(tl(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(adx(cons(y0, y1))))))) MARK(hd(incr(adx(tl(adx(y0)))))) -> c16(MARK(incr(adx(tl(adx(y0)))))) MARK(hd(incr(adx(tl(incr(nats)))))) -> c16(MARK(incr(adx(tl(incr(nats)))))) MARK(hd(incr(adx(tl(incr(adx(y0))))))) -> c16(MARK(incr(adx(tl(incr(adx(y0))))))) MARK(hd(incr(adx(tl(incr(zeros)))))) -> c16(MARK(incr(adx(tl(incr(zeros)))))) MARK(hd(incr(adx(tl(incr(incr(y0))))))) -> c16(MARK(incr(adx(tl(incr(incr(y0))))))) MARK(hd(incr(adx(tl(incr(hd(y0))))))) -> c16(MARK(incr(adx(tl(incr(hd(y0))))))) MARK(hd(incr(adx(tl(incr(tl(y0))))))) -> c16(MARK(incr(adx(tl(incr(tl(y0))))))) MARK(hd(incr(adx(tl(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(incr(cons(y0, y1))))))) MARK(hd(incr(adx(tl(incr(s(y0))))))) -> c16(MARK(incr(adx(tl(incr(s(y0))))))) MARK(hd(incr(adx(tl(incr(y0)))))) -> c16(MARK(incr(adx(tl(incr(y0)))))) MARK(hd(incr(adx(tl(hd(nats)))))) -> c16(MARK(incr(adx(tl(hd(nats)))))) MARK(hd(incr(adx(tl(hd(adx(y0))))))) -> c16(MARK(incr(adx(tl(hd(adx(y0))))))) MARK(hd(incr(adx(tl(hd(incr(y0))))))) -> c16(MARK(incr(adx(tl(hd(incr(y0))))))) MARK(hd(incr(adx(tl(hd(hd(y0))))))) -> c16(MARK(incr(adx(tl(hd(hd(y0))))))) MARK(hd(incr(adx(tl(hd(tl(y0))))))) -> c16(MARK(incr(adx(tl(hd(tl(y0))))))) MARK(hd(incr(adx(tl(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(hd(cons(y0, y1))))))) MARK(hd(incr(adx(tl(hd(y0)))))) -> c16(MARK(incr(adx(tl(hd(y0)))))) MARK(hd(incr(adx(tl(tl(nats)))))) -> c16(MARK(incr(adx(tl(tl(nats)))))) MARK(hd(incr(adx(tl(tl(adx(y0))))))) -> c16(MARK(incr(adx(tl(tl(adx(y0))))))) MARK(hd(incr(adx(tl(tl(incr(y0))))))) -> c16(MARK(incr(adx(tl(tl(incr(y0))))))) MARK(hd(incr(adx(tl(tl(hd(y0))))))) -> c16(MARK(incr(adx(tl(tl(hd(y0))))))) MARK(hd(incr(adx(tl(tl(tl(y0))))))) -> c16(MARK(incr(adx(tl(tl(tl(y0))))))) MARK(hd(incr(adx(tl(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(tl(cons(y0, y1))))))) MARK(hd(incr(adx(tl(tl(y0)))))) -> c16(MARK(incr(adx(tl(tl(y0)))))) MARK(hd(incr(adx(tl(nats))))) -> c16(MARK(incr(adx(tl(nats))))) MARK(hd(incr(adx(hd(adx(0)))))) -> c16(MARK(incr(adx(hd(adx(0)))))) MARK(hd(incr(adx(hd(adx(s(y0))))))) -> c16(MARK(incr(adx(hd(adx(s(y0))))))) MARK(hd(incr(adx(hd(incr(0)))))) -> c16(MARK(incr(adx(hd(incr(0)))))) MARK(hd(incr(adx(hd(incr(s(y0))))))) -> c16(MARK(incr(adx(hd(incr(s(y0))))))) MARK(hd(incr(adx(hd(hd(zeros)))))) -> c16(MARK(incr(adx(hd(hd(zeros)))))) MARK(hd(incr(adx(tl(hd(zeros)))))) -> c16(MARK(incr(adx(tl(hd(zeros)))))) MARK(hd(incr(adx(tl(adx(0)))))) -> c16(MARK(incr(adx(tl(adx(0)))))) MARK(hd(incr(adx(hd(tl(zeros)))))) -> c16(MARK(incr(adx(hd(tl(zeros)))))) MARK(hd(incr(adx(tl(tl(zeros)))))) -> c16(MARK(incr(adx(tl(tl(zeros)))))) MARK(hd(incr(adx(tl(adx(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) MARK(hd(incr(adx(tl(incr(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) MARK(hd(incr(hd(adx(nats))))) -> c16(MARK(incr(hd(adx(nats))))) MARK(hd(incr(hd(adx(zeros))))) -> c16(MARK(incr(hd(adx(zeros))))) MARK(hd(incr(hd(adx(cons(y0, y1)))))) -> c16(MARK(incr(hd(adx(cons(y0, y1)))))) MARK(hd(incr(tl(adx(nats))))) -> c16(MARK(incr(tl(adx(nats))))) MARK(hd(incr(tl(adx(zeros))))) -> c16(MARK(incr(tl(adx(zeros))))) MARK(hd(incr(tl(adx(cons(y0, y1)))))) -> c16(MARK(incr(tl(adx(cons(y0, y1)))))) MARK(hd(incr(tl(incr(s(y0)))))) -> c16(MARK(incr(tl(incr(s(y0)))))) S tuples: MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> 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c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) MARK(tl(cons(z0, adx(y1)))) -> c17(A__TL(cons(z0, adx(y1)))) MARK(tl(cons(z0, incr(y1)))) -> c17(A__TL(cons(z0, incr(y1)))) MARK(tl(cons(z0, hd(cons(y1, y2))))) -> c17(A__TL(cons(z0, hd(cons(y1, y2))))) MARK(tl(cons(z0, tl(cons(y1, y2))))) -> c17(A__TL(cons(z0, tl(cons(y1, y2))))) MARK(tl(cons(z0, hd(adx(nats))))) -> c17(A__TL(cons(z0, hd(adx(nats))))) MARK(tl(cons(z0, hd(adx(adx(y1)))))) -> c17(A__TL(cons(z0, hd(adx(adx(y1)))))) MARK(tl(cons(z0, hd(adx(zeros))))) -> c17(A__TL(cons(z0, hd(adx(zeros))))) MARK(tl(cons(z0, hd(adx(incr(y1)))))) -> c17(A__TL(cons(z0, hd(adx(incr(y1)))))) MARK(tl(cons(z0, hd(adx(hd(y1)))))) -> c17(A__TL(cons(z0, hd(adx(hd(y1)))))) MARK(tl(cons(z0, hd(adx(tl(y1)))))) -> c17(A__TL(cons(z0, hd(adx(tl(y1)))))) MARK(tl(cons(z0, hd(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(adx(cons(y1, y2)))))) MARK(tl(cons(z0, hd(adx(y1))))) -> c17(A__TL(cons(z0, hd(adx(y1))))) MARK(tl(cons(z0, hd(incr(nats))))) -> c17(A__TL(cons(z0, hd(incr(nats))))) MARK(tl(cons(z0, hd(incr(adx(y1)))))) -> c17(A__TL(cons(z0, hd(incr(adx(y1)))))) MARK(tl(cons(z0, hd(incr(zeros))))) -> c17(A__TL(cons(z0, hd(incr(zeros))))) MARK(tl(cons(z0, hd(incr(incr(y1)))))) -> c17(A__TL(cons(z0, hd(incr(incr(y1)))))) MARK(tl(cons(z0, hd(incr(hd(y1)))))) -> c17(A__TL(cons(z0, hd(incr(hd(y1)))))) MARK(tl(cons(z0, hd(incr(tl(y1)))))) -> c17(A__TL(cons(z0, hd(incr(tl(y1)))))) MARK(tl(cons(z0, hd(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(incr(cons(y1, y2)))))) MARK(tl(cons(z0, hd(incr(y1))))) -> c17(A__TL(cons(z0, hd(incr(y1))))) MARK(tl(cons(z0, hd(hd(nats))))) -> c17(A__TL(cons(z0, hd(hd(nats))))) MARK(tl(cons(z0, hd(hd(adx(y1)))))) -> c17(A__TL(cons(z0, hd(hd(adx(y1)))))) MARK(tl(cons(z0, hd(hd(incr(y1)))))) -> c17(A__TL(cons(z0, hd(hd(incr(y1)))))) MARK(tl(cons(z0, hd(hd(hd(y1)))))) -> c17(A__TL(cons(z0, hd(hd(hd(y1)))))) MARK(tl(cons(z0, hd(hd(tl(y1)))))) -> c17(A__TL(cons(z0, hd(hd(tl(y1)))))) MARK(tl(cons(z0, hd(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(hd(cons(y1, y2)))))) MARK(tl(cons(z0, hd(hd(y1))))) -> c17(A__TL(cons(z0, hd(hd(y1))))) MARK(tl(cons(z0, hd(tl(nats))))) -> c17(A__TL(cons(z0, hd(tl(nats))))) MARK(tl(cons(z0, hd(tl(adx(y1)))))) -> c17(A__TL(cons(z0, hd(tl(adx(y1)))))) MARK(tl(cons(z0, hd(tl(zeros))))) -> c17(A__TL(cons(z0, hd(tl(zeros))))) MARK(tl(cons(z0, hd(tl(incr(y1)))))) -> c17(A__TL(cons(z0, hd(tl(incr(y1)))))) MARK(tl(cons(z0, hd(tl(hd(y1)))))) -> c17(A__TL(cons(z0, hd(tl(hd(y1)))))) MARK(tl(cons(z0, hd(tl(tl(y1)))))) -> c17(A__TL(cons(z0, hd(tl(tl(y1)))))) MARK(tl(cons(z0, hd(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(tl(cons(y1, y2)))))) MARK(tl(cons(z0, hd(tl(y1))))) -> c17(A__TL(cons(z0, hd(tl(y1))))) MARK(tl(cons(z0, hd(nats)))) -> c17(A__TL(cons(z0, hd(nats)))) MARK(tl(cons(z0, tl(adx(nats))))) -> c17(A__TL(cons(z0, tl(adx(nats))))) MARK(tl(cons(z0, tl(adx(adx(y1)))))) -> c17(A__TL(cons(z0, tl(adx(adx(y1)))))) MARK(tl(cons(z0, tl(adx(zeros))))) -> c17(A__TL(cons(z0, tl(adx(zeros))))) MARK(tl(cons(z0, tl(adx(incr(y1)))))) -> c17(A__TL(cons(z0, tl(adx(incr(y1)))))) MARK(tl(cons(z0, tl(adx(hd(y1)))))) -> c17(A__TL(cons(z0, tl(adx(hd(y1)))))) MARK(tl(cons(z0, tl(adx(tl(y1)))))) -> c17(A__TL(cons(z0, tl(adx(tl(y1)))))) MARK(tl(cons(z0, tl(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(adx(cons(y1, y2)))))) MARK(tl(cons(z0, tl(adx(s(y1)))))) -> c17(A__TL(cons(z0, tl(adx(s(y1)))))) MARK(tl(cons(z0, tl(adx(y1))))) -> c17(A__TL(cons(z0, tl(adx(y1))))) MARK(tl(cons(z0, tl(incr(nats))))) -> c17(A__TL(cons(z0, tl(incr(nats))))) MARK(tl(cons(z0, tl(incr(adx(y1)))))) -> c17(A__TL(cons(z0, tl(incr(adx(y1)))))) MARK(tl(cons(z0, tl(incr(zeros))))) -> c17(A__TL(cons(z0, tl(incr(zeros))))) MARK(tl(cons(z0, tl(incr(incr(y1)))))) -> c17(A__TL(cons(z0, tl(incr(incr(y1)))))) MARK(tl(cons(z0, tl(incr(hd(y1)))))) -> c17(A__TL(cons(z0, tl(incr(hd(y1)))))) MARK(tl(cons(z0, tl(incr(tl(y1)))))) -> c17(A__TL(cons(z0, tl(incr(tl(y1)))))) MARK(tl(cons(z0, tl(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(incr(cons(y1, y2)))))) MARK(tl(cons(z0, tl(incr(0))))) -> c17(A__TL(cons(z0, tl(incr(0))))) MARK(tl(cons(z0, tl(incr(s(y1)))))) -> c17(A__TL(cons(z0, tl(incr(s(y1)))))) MARK(tl(cons(z0, tl(incr(y1))))) -> c17(A__TL(cons(z0, tl(incr(y1))))) MARK(tl(cons(z0, tl(hd(nats))))) -> c17(A__TL(cons(z0, tl(hd(nats))))) MARK(tl(cons(z0, tl(hd(adx(y1)))))) -> c17(A__TL(cons(z0, tl(hd(adx(y1)))))) MARK(tl(cons(z0, tl(hd(incr(y1)))))) -> c17(A__TL(cons(z0, tl(hd(incr(y1)))))) MARK(tl(cons(z0, tl(hd(hd(y1)))))) -> c17(A__TL(cons(z0, tl(hd(hd(y1)))))) MARK(tl(cons(z0, tl(hd(tl(y1)))))) -> c17(A__TL(cons(z0, tl(hd(tl(y1)))))) MARK(tl(cons(z0, tl(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(hd(cons(y1, y2)))))) MARK(tl(cons(z0, tl(hd(y1))))) -> c17(A__TL(cons(z0, tl(hd(y1))))) MARK(tl(cons(z0, tl(tl(nats))))) -> c17(A__TL(cons(z0, tl(tl(nats))))) MARK(tl(cons(z0, tl(tl(adx(y1)))))) -> c17(A__TL(cons(z0, tl(tl(adx(y1)))))) MARK(tl(cons(z0, tl(tl(zeros))))) -> c17(A__TL(cons(z0, tl(tl(zeros))))) MARK(tl(cons(z0, tl(tl(incr(y1)))))) -> c17(A__TL(cons(z0, tl(tl(incr(y1)))))) MARK(tl(cons(z0, tl(tl(hd(y1)))))) -> c17(A__TL(cons(z0, tl(tl(hd(y1)))))) MARK(tl(cons(z0, tl(tl(tl(y1)))))) -> c17(A__TL(cons(z0, tl(tl(tl(y1)))))) MARK(tl(cons(z0, tl(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(tl(cons(y1, y2)))))) MARK(tl(cons(z0, tl(tl(y1))))) -> c17(A__TL(cons(z0, tl(tl(y1))))) MARK(tl(cons(z0, tl(nats)))) -> c17(A__TL(cons(z0, tl(nats)))) MARK(tl(cons(z0, hd(adx(0))))) -> c17(A__TL(cons(z0, hd(adx(0))))) MARK(tl(cons(z0, hd(adx(s(y1)))))) -> c17(A__TL(cons(z0, hd(adx(s(y1)))))) MARK(tl(cons(z0, hd(incr(0))))) -> c17(A__TL(cons(z0, hd(incr(0))))) MARK(tl(cons(z0, hd(incr(s(y1)))))) -> c17(A__TL(cons(z0, hd(incr(s(y1)))))) MARK(tl(cons(z0, hd(hd(zeros))))) -> c17(A__TL(cons(z0, hd(hd(zeros))))) MARK(tl(cons(z0, tl(hd(zeros))))) -> c17(A__TL(cons(z0, tl(hd(zeros))))) MARK(tl(cons(z0, tl(adx(0))))) -> c17(A__TL(cons(z0, tl(adx(0))))) MARK(hd(adx(adx(y0)))) -> c16(MARK(adx(adx(y0)))) MARK(hd(adx(incr(y0)))) -> c16(MARK(adx(incr(y0)))) MARK(hd(adx(hd(cons(y0, y1))))) -> c16(MARK(adx(hd(cons(y0, y1))))) MARK(hd(adx(tl(cons(y0, y1))))) -> c16(MARK(adx(tl(cons(y0, y1))))) MARK(hd(adx(hd(adx(nats))))) -> c16(MARK(adx(hd(adx(nats))))) MARK(hd(adx(hd(adx(adx(y0)))))) -> c16(MARK(adx(hd(adx(adx(y0)))))) MARK(hd(adx(hd(adx(zeros))))) -> c16(MARK(adx(hd(adx(zeros))))) MARK(hd(adx(hd(adx(incr(y0)))))) -> c16(MARK(adx(hd(adx(incr(y0)))))) MARK(hd(adx(hd(adx(hd(y0)))))) -> c16(MARK(adx(hd(adx(hd(y0)))))) MARK(hd(adx(hd(adx(tl(y0)))))) -> c16(MARK(adx(hd(adx(tl(y0)))))) MARK(hd(adx(hd(adx(cons(y0, y1)))))) -> c16(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(hd(adx(hd(adx(y0))))) -> c16(MARK(adx(hd(adx(y0))))) MARK(hd(adx(hd(incr(nats))))) -> c16(MARK(adx(hd(incr(nats))))) MARK(hd(adx(hd(incr(adx(y0)))))) -> c16(MARK(adx(hd(incr(adx(y0)))))) MARK(hd(adx(hd(incr(zeros))))) -> c16(MARK(adx(hd(incr(zeros))))) MARK(hd(adx(hd(incr(incr(y0)))))) -> c16(MARK(adx(hd(incr(incr(y0)))))) MARK(hd(adx(hd(incr(hd(y0)))))) -> c16(MARK(adx(hd(incr(hd(y0)))))) MARK(hd(adx(hd(incr(tl(y0)))))) -> c16(MARK(adx(hd(incr(tl(y0)))))) MARK(hd(adx(hd(incr(cons(y0, y1)))))) -> c16(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(hd(adx(hd(incr(y0))))) -> c16(MARK(adx(hd(incr(y0))))) MARK(hd(adx(hd(hd(nats))))) -> c16(MARK(adx(hd(hd(nats))))) MARK(hd(adx(hd(hd(adx(y0)))))) -> c16(MARK(adx(hd(hd(adx(y0)))))) MARK(hd(adx(hd(hd(incr(y0)))))) -> c16(MARK(adx(hd(hd(incr(y0)))))) MARK(hd(adx(hd(hd(hd(y0)))))) -> c16(MARK(adx(hd(hd(hd(y0)))))) MARK(hd(adx(hd(hd(tl(y0)))))) -> c16(MARK(adx(hd(hd(tl(y0)))))) MARK(hd(adx(hd(hd(cons(y0, y1)))))) -> c16(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(hd(adx(hd(hd(y0))))) -> c16(MARK(adx(hd(hd(y0))))) MARK(hd(adx(hd(tl(nats))))) -> c16(MARK(adx(hd(tl(nats))))) MARK(hd(adx(hd(tl(adx(y0)))))) -> c16(MARK(adx(hd(tl(adx(y0)))))) MARK(hd(adx(hd(tl(incr(y0)))))) -> c16(MARK(adx(hd(tl(incr(y0)))))) MARK(hd(adx(hd(tl(hd(y0)))))) -> c16(MARK(adx(hd(tl(hd(y0)))))) MARK(hd(adx(hd(tl(tl(y0)))))) -> c16(MARK(adx(hd(tl(tl(y0)))))) MARK(hd(adx(hd(tl(cons(y0, y1)))))) -> c16(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(hd(adx(hd(tl(y0))))) -> c16(MARK(adx(hd(tl(y0))))) MARK(hd(adx(hd(nats)))) -> c16(MARK(adx(hd(nats)))) MARK(hd(adx(tl(adx(nats))))) -> c16(MARK(adx(tl(adx(nats))))) MARK(hd(adx(tl(adx(adx(y0)))))) -> c16(MARK(adx(tl(adx(adx(y0)))))) MARK(hd(adx(tl(adx(zeros))))) -> c16(MARK(adx(tl(adx(zeros))))) MARK(hd(adx(tl(adx(incr(y0)))))) -> c16(MARK(adx(tl(adx(incr(y0)))))) MARK(hd(adx(tl(adx(hd(y0)))))) -> c16(MARK(adx(tl(adx(hd(y0)))))) MARK(hd(adx(tl(adx(tl(y0)))))) -> c16(MARK(adx(tl(adx(tl(y0)))))) MARK(hd(adx(tl(adx(cons(y0, y1)))))) -> c16(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(hd(adx(tl(adx(y0))))) -> c16(MARK(adx(tl(adx(y0))))) MARK(hd(adx(tl(incr(nats))))) -> c16(MARK(adx(tl(incr(nats))))) MARK(hd(adx(tl(incr(adx(y0)))))) -> c16(MARK(adx(tl(incr(adx(y0)))))) MARK(hd(adx(tl(incr(zeros))))) -> c16(MARK(adx(tl(incr(zeros))))) MARK(hd(adx(tl(incr(incr(y0)))))) -> c16(MARK(adx(tl(incr(incr(y0)))))) MARK(hd(adx(tl(incr(hd(y0)))))) -> c16(MARK(adx(tl(incr(hd(y0)))))) MARK(hd(adx(tl(incr(tl(y0)))))) -> c16(MARK(adx(tl(incr(tl(y0)))))) MARK(hd(adx(tl(incr(cons(y0, y1)))))) -> c16(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(hd(adx(tl(incr(s(y0)))))) -> c16(MARK(adx(tl(incr(s(y0)))))) MARK(hd(adx(tl(incr(y0))))) -> c16(MARK(adx(tl(incr(y0))))) MARK(hd(adx(tl(hd(nats))))) -> c16(MARK(adx(tl(hd(nats))))) MARK(hd(adx(tl(hd(adx(y0)))))) -> c16(MARK(adx(tl(hd(adx(y0)))))) MARK(hd(adx(tl(hd(incr(y0)))))) -> c16(MARK(adx(tl(hd(incr(y0)))))) MARK(hd(adx(tl(hd(hd(y0)))))) -> c16(MARK(adx(tl(hd(hd(y0)))))) MARK(hd(adx(tl(hd(tl(y0)))))) -> c16(MARK(adx(tl(hd(tl(y0)))))) MARK(hd(adx(tl(hd(cons(y0, y1)))))) -> c16(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(hd(adx(tl(hd(y0))))) -> c16(MARK(adx(tl(hd(y0))))) MARK(hd(adx(tl(tl(nats))))) -> c16(MARK(adx(tl(tl(nats))))) MARK(hd(adx(tl(tl(adx(y0)))))) -> c16(MARK(adx(tl(tl(adx(y0)))))) MARK(hd(adx(tl(tl(incr(y0)))))) -> c16(MARK(adx(tl(tl(incr(y0)))))) MARK(hd(adx(tl(tl(hd(y0)))))) -> c16(MARK(adx(tl(tl(hd(y0)))))) MARK(hd(adx(tl(tl(tl(y0)))))) -> c16(MARK(adx(tl(tl(tl(y0)))))) MARK(hd(adx(tl(tl(cons(y0, y1)))))) -> c16(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(hd(adx(tl(tl(y0))))) -> c16(MARK(adx(tl(tl(y0))))) MARK(hd(adx(tl(nats)))) -> c16(MARK(adx(tl(nats)))) MARK(hd(adx(hd(adx(0))))) -> c16(MARK(adx(hd(adx(0))))) MARK(hd(adx(hd(adx(s(y0)))))) -> c16(MARK(adx(hd(adx(s(y0)))))) MARK(hd(adx(hd(incr(0))))) -> c16(MARK(adx(hd(incr(0))))) MARK(hd(adx(hd(incr(s(y0)))))) -> c16(MARK(adx(hd(incr(s(y0)))))) MARK(hd(adx(hd(hd(zeros))))) -> c16(MARK(adx(hd(hd(zeros))))) MARK(hd(adx(tl(hd(zeros))))) -> c16(MARK(adx(tl(hd(zeros))))) MARK(hd(adx(tl(adx(0))))) -> c16(MARK(adx(tl(adx(0))))) MARK(hd(adx(hd(tl(zeros))))) -> c16(MARK(adx(hd(tl(zeros))))) MARK(hd(adx(tl(tl(zeros))))) -> c16(MARK(adx(tl(tl(zeros))))) MARK(hd(adx(tl(adx(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) MARK(hd(adx(tl(incr(0))))) -> c16(MARK(adx(tl(incr(0))))) MARK(hd(incr(incr(y0)))) -> c16(MARK(incr(incr(y0)))) MARK(hd(incr(hd(cons(y0, y1))))) -> c16(MARK(incr(hd(cons(y0, y1))))) MARK(hd(incr(tl(cons(y0, y1))))) -> c16(MARK(incr(tl(cons(y0, y1))))) MARK(hd(incr(hd(adx(adx(y0)))))) -> c16(MARK(incr(hd(adx(adx(y0)))))) MARK(hd(incr(hd(adx(incr(y0)))))) -> c16(MARK(incr(hd(adx(incr(y0)))))) MARK(hd(incr(hd(adx(hd(y0)))))) -> c16(MARK(incr(hd(adx(hd(y0)))))) MARK(hd(incr(hd(adx(tl(y0)))))) -> c16(MARK(incr(hd(adx(tl(y0)))))) MARK(hd(incr(hd(adx(y0))))) -> c16(MARK(incr(hd(adx(y0))))) MARK(hd(incr(hd(incr(nats))))) -> c16(MARK(incr(hd(incr(nats))))) MARK(hd(incr(hd(incr(adx(y0)))))) -> c16(MARK(incr(hd(incr(adx(y0)))))) MARK(hd(incr(hd(incr(zeros))))) -> c16(MARK(incr(hd(incr(zeros))))) MARK(hd(incr(hd(incr(incr(y0)))))) -> c16(MARK(incr(hd(incr(incr(y0)))))) MARK(hd(incr(hd(incr(hd(y0)))))) -> c16(MARK(incr(hd(incr(hd(y0)))))) MARK(hd(incr(hd(incr(tl(y0)))))) -> c16(MARK(incr(hd(incr(tl(y0)))))) MARK(hd(incr(hd(incr(cons(y0, y1)))))) -> c16(MARK(incr(hd(incr(cons(y0, y1)))))) MARK(hd(incr(hd(incr(y0))))) -> c16(MARK(incr(hd(incr(y0))))) MARK(hd(incr(hd(hd(nats))))) -> c16(MARK(incr(hd(hd(nats))))) MARK(hd(incr(hd(hd(adx(y0)))))) -> c16(MARK(incr(hd(hd(adx(y0)))))) MARK(hd(incr(hd(hd(incr(y0)))))) -> c16(MARK(incr(hd(hd(incr(y0)))))) MARK(hd(incr(hd(hd(hd(y0)))))) -> c16(MARK(incr(hd(hd(hd(y0)))))) MARK(hd(incr(hd(hd(tl(y0)))))) -> c16(MARK(incr(hd(hd(tl(y0)))))) MARK(hd(incr(hd(hd(cons(y0, y1)))))) -> c16(MARK(incr(hd(hd(cons(y0, y1)))))) MARK(hd(incr(hd(hd(y0))))) -> c16(MARK(incr(hd(hd(y0))))) MARK(hd(incr(hd(tl(nats))))) -> c16(MARK(incr(hd(tl(nats))))) MARK(hd(incr(hd(tl(adx(y0)))))) -> c16(MARK(incr(hd(tl(adx(y0)))))) MARK(hd(incr(hd(tl(incr(y0)))))) -> c16(MARK(incr(hd(tl(incr(y0)))))) MARK(hd(incr(hd(tl(hd(y0)))))) -> c16(MARK(incr(hd(tl(hd(y0)))))) MARK(hd(incr(hd(tl(tl(y0)))))) -> c16(MARK(incr(hd(tl(tl(y0)))))) MARK(hd(incr(hd(tl(cons(y0, y1)))))) -> c16(MARK(incr(hd(tl(cons(y0, y1)))))) MARK(hd(incr(hd(tl(y0))))) -> c16(MARK(incr(hd(tl(y0))))) MARK(hd(incr(hd(nats)))) -> c16(MARK(incr(hd(nats)))) MARK(hd(incr(tl(adx(adx(y0)))))) -> c16(MARK(incr(tl(adx(adx(y0)))))) MARK(hd(incr(tl(adx(incr(y0)))))) -> c16(MARK(incr(tl(adx(incr(y0)))))) MARK(hd(incr(tl(adx(hd(y0)))))) -> c16(MARK(incr(tl(adx(hd(y0)))))) MARK(hd(incr(tl(adx(tl(y0)))))) -> c16(MARK(incr(tl(adx(tl(y0)))))) MARK(hd(incr(tl(adx(y0))))) -> c16(MARK(incr(tl(adx(y0))))) MARK(hd(incr(tl(incr(nats))))) -> c16(MARK(incr(tl(incr(nats))))) MARK(hd(incr(tl(incr(adx(y0)))))) -> c16(MARK(incr(tl(incr(adx(y0)))))) MARK(hd(incr(tl(incr(zeros))))) -> c16(MARK(incr(tl(incr(zeros))))) MARK(hd(incr(tl(incr(incr(y0)))))) -> c16(MARK(incr(tl(incr(incr(y0)))))) MARK(hd(incr(tl(incr(hd(y0)))))) -> c16(MARK(incr(tl(incr(hd(y0)))))) MARK(hd(incr(tl(incr(tl(y0)))))) -> c16(MARK(incr(tl(incr(tl(y0)))))) MARK(hd(incr(tl(incr(cons(y0, y1)))))) -> c16(MARK(incr(tl(incr(cons(y0, y1)))))) MARK(hd(incr(tl(incr(y0))))) -> c16(MARK(incr(tl(incr(y0))))) MARK(hd(incr(tl(hd(nats))))) -> c16(MARK(incr(tl(hd(nats))))) MARK(hd(incr(tl(hd(adx(y0)))))) -> c16(MARK(incr(tl(hd(adx(y0)))))) MARK(hd(incr(tl(hd(incr(y0)))))) -> c16(MARK(incr(tl(hd(incr(y0)))))) MARK(hd(incr(tl(hd(hd(y0)))))) -> c16(MARK(incr(tl(hd(hd(y0)))))) MARK(hd(incr(tl(hd(tl(y0)))))) -> c16(MARK(incr(tl(hd(tl(y0)))))) MARK(hd(incr(tl(hd(cons(y0, y1)))))) -> c16(MARK(incr(tl(hd(cons(y0, y1)))))) MARK(hd(incr(tl(hd(y0))))) -> c16(MARK(incr(tl(hd(y0))))) MARK(hd(incr(tl(tl(nats))))) -> c16(MARK(incr(tl(tl(nats))))) MARK(hd(incr(tl(tl(adx(y0)))))) -> c16(MARK(incr(tl(tl(adx(y0)))))) MARK(hd(incr(tl(tl(incr(y0)))))) -> c16(MARK(incr(tl(tl(incr(y0)))))) MARK(hd(incr(tl(tl(hd(y0)))))) -> c16(MARK(incr(tl(tl(hd(y0)))))) MARK(hd(incr(tl(tl(tl(y0)))))) -> c16(MARK(incr(tl(tl(tl(y0)))))) MARK(hd(incr(tl(tl(cons(y0, y1)))))) -> c16(MARK(incr(tl(tl(cons(y0, y1)))))) MARK(hd(incr(tl(tl(y0))))) -> c16(MARK(incr(tl(tl(y0))))) MARK(hd(incr(tl(nats)))) -> c16(MARK(incr(tl(nats)))) MARK(hd(incr(hd(incr(0))))) -> c16(MARK(incr(hd(incr(0))))) MARK(hd(incr(hd(incr(s(y0)))))) -> c16(MARK(incr(hd(incr(s(y0)))))) MARK(hd(incr(hd(hd(zeros))))) -> c16(MARK(incr(hd(hd(zeros))))) MARK(hd(incr(tl(hd(zeros))))) -> c16(MARK(incr(tl(hd(zeros))))) MARK(hd(incr(hd(tl(zeros))))) -> c16(MARK(incr(hd(tl(zeros))))) MARK(hd(incr(tl(tl(zeros))))) -> c16(MARK(incr(tl(tl(zeros))))) MARK(hd(incr(tl(incr(0))))) -> c16(MARK(incr(tl(incr(0))))) MARK(hd(incr(adx(adx(y0))))) -> c16(MARK(incr(adx(adx(y0))))) MARK(hd(incr(adx(incr(y0))))) -> c16(MARK(incr(adx(incr(y0))))) MARK(hd(incr(adx(hd(cons(y0, y1)))))) -> c16(MARK(incr(adx(hd(cons(y0, y1)))))) MARK(hd(incr(adx(tl(cons(y0, y1)))))) -> c16(MARK(incr(adx(tl(cons(y0, y1)))))) MARK(hd(incr(adx(hd(adx(nats)))))) -> c16(MARK(incr(adx(hd(adx(nats)))))) MARK(hd(incr(adx(hd(adx(adx(y0))))))) -> c16(MARK(incr(adx(hd(adx(adx(y0))))))) MARK(hd(incr(adx(hd(adx(zeros)))))) -> c16(MARK(incr(adx(hd(adx(zeros)))))) MARK(hd(incr(adx(hd(adx(incr(y0))))))) -> c16(MARK(incr(adx(hd(adx(incr(y0))))))) MARK(hd(incr(adx(hd(adx(hd(y0))))))) -> c16(MARK(incr(adx(hd(adx(hd(y0))))))) MARK(hd(incr(adx(hd(adx(tl(y0))))))) -> c16(MARK(incr(adx(hd(adx(tl(y0))))))) MARK(hd(incr(adx(hd(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(adx(cons(y0, y1))))))) MARK(hd(incr(adx(hd(adx(y0)))))) -> c16(MARK(incr(adx(hd(adx(y0)))))) MARK(hd(incr(adx(hd(incr(nats)))))) -> c16(MARK(incr(adx(hd(incr(nats)))))) MARK(hd(incr(adx(hd(incr(adx(y0))))))) -> c16(MARK(incr(adx(hd(incr(adx(y0))))))) MARK(hd(incr(adx(hd(incr(zeros)))))) -> c16(MARK(incr(adx(hd(incr(zeros)))))) MARK(hd(incr(adx(hd(incr(incr(y0))))))) -> c16(MARK(incr(adx(hd(incr(incr(y0))))))) MARK(hd(incr(adx(hd(incr(hd(y0))))))) -> c16(MARK(incr(adx(hd(incr(hd(y0))))))) MARK(hd(incr(adx(hd(incr(tl(y0))))))) -> c16(MARK(incr(adx(hd(incr(tl(y0))))))) MARK(hd(incr(adx(hd(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(incr(cons(y0, y1))))))) MARK(hd(incr(adx(hd(incr(y0)))))) -> c16(MARK(incr(adx(hd(incr(y0)))))) MARK(hd(incr(adx(hd(hd(nats)))))) -> c16(MARK(incr(adx(hd(hd(nats)))))) MARK(hd(incr(adx(hd(hd(adx(y0))))))) -> c16(MARK(incr(adx(hd(hd(adx(y0))))))) MARK(hd(incr(adx(hd(hd(incr(y0))))))) -> c16(MARK(incr(adx(hd(hd(incr(y0))))))) MARK(hd(incr(adx(hd(hd(hd(y0))))))) -> c16(MARK(incr(adx(hd(hd(hd(y0))))))) MARK(hd(incr(adx(hd(hd(tl(y0))))))) -> c16(MARK(incr(adx(hd(hd(tl(y0))))))) MARK(hd(incr(adx(hd(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(hd(cons(y0, y1))))))) MARK(hd(incr(adx(hd(hd(y0)))))) -> c16(MARK(incr(adx(hd(hd(y0)))))) MARK(hd(incr(adx(hd(tl(nats)))))) -> c16(MARK(incr(adx(hd(tl(nats)))))) MARK(hd(incr(adx(hd(tl(adx(y0))))))) -> c16(MARK(incr(adx(hd(tl(adx(y0))))))) MARK(hd(incr(adx(hd(tl(incr(y0))))))) -> c16(MARK(incr(adx(hd(tl(incr(y0))))))) MARK(hd(incr(adx(hd(tl(hd(y0))))))) -> c16(MARK(incr(adx(hd(tl(hd(y0))))))) MARK(hd(incr(adx(hd(tl(tl(y0))))))) -> c16(MARK(incr(adx(hd(tl(tl(y0))))))) MARK(hd(incr(adx(hd(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(tl(cons(y0, y1))))))) MARK(hd(incr(adx(hd(tl(y0)))))) -> c16(MARK(incr(adx(hd(tl(y0)))))) MARK(hd(incr(adx(hd(nats))))) -> c16(MARK(incr(adx(hd(nats))))) MARK(hd(incr(adx(tl(adx(nats)))))) -> c16(MARK(incr(adx(tl(adx(nats)))))) MARK(hd(incr(adx(tl(adx(adx(y0))))))) -> c16(MARK(incr(adx(tl(adx(adx(y0))))))) MARK(hd(incr(adx(tl(adx(zeros)))))) -> c16(MARK(incr(adx(tl(adx(zeros)))))) MARK(hd(incr(adx(tl(adx(incr(y0))))))) -> c16(MARK(incr(adx(tl(adx(incr(y0))))))) MARK(hd(incr(adx(tl(adx(hd(y0))))))) -> c16(MARK(incr(adx(tl(adx(hd(y0))))))) MARK(hd(incr(adx(tl(adx(tl(y0))))))) -> c16(MARK(incr(adx(tl(adx(tl(y0))))))) MARK(hd(incr(adx(tl(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(adx(cons(y0, y1))))))) MARK(hd(incr(adx(tl(adx(y0)))))) -> c16(MARK(incr(adx(tl(adx(y0)))))) MARK(hd(incr(adx(tl(incr(nats)))))) -> c16(MARK(incr(adx(tl(incr(nats)))))) MARK(hd(incr(adx(tl(incr(adx(y0))))))) -> c16(MARK(incr(adx(tl(incr(adx(y0))))))) MARK(hd(incr(adx(tl(incr(zeros)))))) -> c16(MARK(incr(adx(tl(incr(zeros)))))) MARK(hd(incr(adx(tl(incr(incr(y0))))))) -> c16(MARK(incr(adx(tl(incr(incr(y0))))))) MARK(hd(incr(adx(tl(incr(hd(y0))))))) -> c16(MARK(incr(adx(tl(incr(hd(y0))))))) MARK(hd(incr(adx(tl(incr(tl(y0))))))) -> c16(MARK(incr(adx(tl(incr(tl(y0))))))) MARK(hd(incr(adx(tl(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(incr(cons(y0, y1))))))) MARK(hd(incr(adx(tl(incr(s(y0))))))) -> c16(MARK(incr(adx(tl(incr(s(y0))))))) MARK(hd(incr(adx(tl(incr(y0)))))) -> c16(MARK(incr(adx(tl(incr(y0)))))) MARK(hd(incr(adx(tl(hd(nats)))))) -> c16(MARK(incr(adx(tl(hd(nats)))))) MARK(hd(incr(adx(tl(hd(adx(y0))))))) -> c16(MARK(incr(adx(tl(hd(adx(y0))))))) MARK(hd(incr(adx(tl(hd(incr(y0))))))) -> c16(MARK(incr(adx(tl(hd(incr(y0))))))) MARK(hd(incr(adx(tl(hd(hd(y0))))))) -> c16(MARK(incr(adx(tl(hd(hd(y0))))))) MARK(hd(incr(adx(tl(hd(tl(y0))))))) -> c16(MARK(incr(adx(tl(hd(tl(y0))))))) MARK(hd(incr(adx(tl(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(hd(cons(y0, y1))))))) MARK(hd(incr(adx(tl(hd(y0)))))) -> c16(MARK(incr(adx(tl(hd(y0)))))) MARK(hd(incr(adx(tl(tl(nats)))))) -> c16(MARK(incr(adx(tl(tl(nats)))))) MARK(hd(incr(adx(tl(tl(adx(y0))))))) -> c16(MARK(incr(adx(tl(tl(adx(y0))))))) MARK(hd(incr(adx(tl(tl(incr(y0))))))) -> c16(MARK(incr(adx(tl(tl(incr(y0))))))) MARK(hd(incr(adx(tl(tl(hd(y0))))))) -> c16(MARK(incr(adx(tl(tl(hd(y0))))))) MARK(hd(incr(adx(tl(tl(tl(y0))))))) -> c16(MARK(incr(adx(tl(tl(tl(y0))))))) MARK(hd(incr(adx(tl(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(tl(cons(y0, y1))))))) MARK(hd(incr(adx(tl(tl(y0)))))) -> c16(MARK(incr(adx(tl(tl(y0)))))) MARK(hd(incr(adx(tl(nats))))) -> c16(MARK(incr(adx(tl(nats))))) MARK(hd(incr(adx(hd(adx(0)))))) -> c16(MARK(incr(adx(hd(adx(0)))))) MARK(hd(incr(adx(hd(adx(s(y0))))))) -> c16(MARK(incr(adx(hd(adx(s(y0))))))) MARK(hd(incr(adx(hd(incr(0)))))) -> c16(MARK(incr(adx(hd(incr(0)))))) MARK(hd(incr(adx(hd(incr(s(y0))))))) -> c16(MARK(incr(adx(hd(incr(s(y0))))))) MARK(hd(incr(adx(hd(hd(zeros)))))) -> c16(MARK(incr(adx(hd(hd(zeros)))))) MARK(hd(incr(adx(tl(hd(zeros)))))) -> c16(MARK(incr(adx(tl(hd(zeros)))))) MARK(hd(incr(adx(tl(adx(0)))))) -> c16(MARK(incr(adx(tl(adx(0)))))) MARK(hd(incr(adx(hd(tl(zeros)))))) -> c16(MARK(incr(adx(hd(tl(zeros)))))) MARK(hd(incr(adx(tl(tl(zeros)))))) -> c16(MARK(incr(adx(tl(tl(zeros)))))) MARK(hd(incr(adx(tl(adx(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) MARK(hd(incr(adx(tl(incr(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) MARK(hd(incr(hd(adx(nats))))) -> c16(MARK(incr(hd(adx(nats))))) MARK(hd(incr(hd(adx(zeros))))) -> c16(MARK(incr(hd(adx(zeros))))) MARK(hd(incr(hd(adx(cons(y0, y1)))))) -> c16(MARK(incr(hd(adx(cons(y0, y1)))))) MARK(hd(incr(tl(adx(nats))))) -> c16(MARK(incr(tl(adx(nats))))) MARK(hd(incr(tl(adx(zeros))))) -> c16(MARK(incr(tl(adx(zeros))))) MARK(hd(incr(tl(adx(cons(y0, y1)))))) -> c16(MARK(incr(tl(adx(cons(y0, y1)))))) MARK(hd(incr(tl(incr(s(y0)))))) -> c16(MARK(incr(tl(incr(s(y0)))))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c16_2, c16_1, c17_2, c17_1, c8_1, c10_1, c13_1, c15_1 ---------------------------------------- (213) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(hd(hd(x0))) -> c16(MARK(hd(x0))) by MARK(hd(hd(adx(adx(y0))))) -> c16(MARK(hd(adx(adx(y0))))) MARK(hd(hd(adx(incr(y0))))) -> c16(MARK(hd(adx(incr(y0))))) MARK(hd(hd(adx(hd(y0))))) -> c16(MARK(hd(adx(hd(y0))))) MARK(hd(hd(adx(tl(y0))))) -> c16(MARK(hd(adx(tl(y0))))) MARK(hd(hd(incr(adx(y0))))) -> c16(MARK(hd(incr(adx(y0))))) MARK(hd(hd(incr(incr(y0))))) -> c16(MARK(hd(incr(incr(y0))))) MARK(hd(hd(incr(hd(y0))))) -> c16(MARK(hd(incr(hd(y0))))) MARK(hd(hd(incr(tl(y0))))) -> c16(MARK(hd(incr(tl(y0))))) MARK(hd(hd(hd(nats)))) -> c16(MARK(hd(hd(nats)))) MARK(hd(hd(hd(adx(y0))))) -> c16(MARK(hd(hd(adx(y0))))) MARK(hd(hd(hd(incr(y0))))) -> c16(MARK(hd(hd(incr(y0))))) MARK(hd(hd(hd(hd(y0))))) -> c16(MARK(hd(hd(hd(y0))))) MARK(hd(hd(hd(tl(y0))))) -> c16(MARK(hd(hd(tl(y0))))) MARK(hd(hd(hd(cons(y0, y1))))) -> c16(MARK(hd(hd(cons(y0, y1))))) MARK(hd(hd(hd(y0)))) -> c16(MARK(hd(hd(y0)))) MARK(hd(hd(tl(nats)))) -> c16(MARK(hd(tl(nats)))) MARK(hd(hd(tl(adx(y0))))) -> c16(MARK(hd(tl(adx(y0))))) MARK(hd(hd(tl(incr(y0))))) -> c16(MARK(hd(tl(incr(y0))))) MARK(hd(hd(tl(hd(y0))))) -> c16(MARK(hd(tl(hd(y0))))) MARK(hd(hd(tl(tl(y0))))) -> c16(MARK(hd(tl(tl(y0))))) MARK(hd(hd(tl(cons(y0, y1))))) -> c16(MARK(hd(tl(cons(y0, y1))))) MARK(hd(hd(tl(y0)))) -> c16(MARK(hd(tl(y0)))) MARK(hd(hd(nats))) -> c16(MARK(hd(nats))) MARK(hd(hd(hd(zeros)))) -> c16(MARK(hd(hd(zeros)))) MARK(hd(hd(tl(zeros)))) -> c16(MARK(hd(tl(zeros)))) MARK(hd(hd(adx(nats)))) -> c16(MARK(hd(adx(nats)))) MARK(hd(hd(adx(zeros)))) -> c16(MARK(hd(adx(zeros)))) MARK(hd(hd(adx(cons(y0, y1))))) -> c16(MARK(hd(adx(cons(y0, y1))))) MARK(hd(hd(incr(nats)))) -> c16(MARK(hd(incr(nats)))) MARK(hd(hd(incr(zeros)))) -> c16(MARK(hd(incr(zeros)))) MARK(hd(hd(cons(adx(y0), y1)))) -> c16(MARK(hd(cons(adx(y0), y1)))) MARK(hd(hd(cons(incr(y0), y1)))) -> c16(MARK(hd(cons(incr(y0), y1)))) MARK(hd(hd(cons(hd(cons(y0, y1)), y2)))) -> c16(MARK(hd(cons(hd(cons(y0, y1)), y2)))) MARK(hd(hd(cons(tl(cons(y0, y1)), y2)))) -> c16(MARK(hd(cons(tl(cons(y0, y1)), y2)))) MARK(hd(hd(cons(hd(adx(nats)), y0)))) -> c16(MARK(hd(cons(hd(adx(nats)), y0)))) MARK(hd(hd(cons(hd(adx(adx(y0))), y1)))) -> c16(MARK(hd(cons(hd(adx(adx(y0))), y1)))) MARK(hd(hd(cons(hd(adx(zeros)), y0)))) -> c16(MARK(hd(cons(hd(adx(zeros)), y0)))) MARK(hd(hd(cons(hd(adx(incr(y0))), y1)))) -> c16(MARK(hd(cons(hd(adx(incr(y0))), y1)))) MARK(hd(hd(cons(hd(adx(hd(y0))), y1)))) -> c16(MARK(hd(cons(hd(adx(hd(y0))), y1)))) MARK(hd(hd(cons(hd(adx(tl(y0))), y1)))) -> c16(MARK(hd(cons(hd(adx(tl(y0))), y1)))) MARK(hd(hd(cons(hd(adx(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(hd(adx(cons(y0, y1))), y2)))) MARK(hd(hd(cons(hd(adx(y0)), y1)))) -> c16(MARK(hd(cons(hd(adx(y0)), y1)))) MARK(hd(hd(cons(hd(incr(nats)), y0)))) -> c16(MARK(hd(cons(hd(incr(nats)), y0)))) MARK(hd(hd(cons(hd(incr(adx(y0))), y1)))) -> c16(MARK(hd(cons(hd(incr(adx(y0))), y1)))) MARK(hd(hd(cons(hd(incr(zeros)), y0)))) -> c16(MARK(hd(cons(hd(incr(zeros)), y0)))) MARK(hd(hd(cons(hd(incr(incr(y0))), y1)))) -> c16(MARK(hd(cons(hd(incr(incr(y0))), y1)))) MARK(hd(hd(cons(hd(incr(hd(y0))), y1)))) -> c16(MARK(hd(cons(hd(incr(hd(y0))), y1)))) MARK(hd(hd(cons(hd(incr(tl(y0))), y1)))) -> c16(MARK(hd(cons(hd(incr(tl(y0))), y1)))) MARK(hd(hd(cons(hd(incr(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(hd(incr(cons(y0, y1))), y2)))) MARK(hd(hd(cons(hd(incr(y0)), y1)))) -> c16(MARK(hd(cons(hd(incr(y0)), y1)))) MARK(hd(hd(cons(hd(hd(nats)), y0)))) -> c16(MARK(hd(cons(hd(hd(nats)), y0)))) MARK(hd(hd(cons(hd(hd(adx(y0))), y1)))) -> c16(MARK(hd(cons(hd(hd(adx(y0))), y1)))) MARK(hd(hd(cons(hd(hd(zeros)), y0)))) -> c16(MARK(hd(cons(hd(hd(zeros)), y0)))) MARK(hd(hd(cons(hd(hd(incr(y0))), y1)))) -> c16(MARK(hd(cons(hd(hd(incr(y0))), y1)))) MARK(hd(hd(cons(hd(hd(hd(y0))), y1)))) -> c16(MARK(hd(cons(hd(hd(hd(y0))), y1)))) MARK(hd(hd(cons(hd(hd(tl(y0))), y1)))) -> c16(MARK(hd(cons(hd(hd(tl(y0))), y1)))) MARK(hd(hd(cons(hd(hd(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(hd(hd(cons(y0, y1))), y2)))) MARK(hd(hd(cons(hd(hd(y0)), y1)))) -> c16(MARK(hd(cons(hd(hd(y0)), y1)))) MARK(hd(hd(cons(hd(tl(nats)), y0)))) -> c16(MARK(hd(cons(hd(tl(nats)), y0)))) MARK(hd(hd(cons(hd(tl(adx(y0))), y1)))) -> c16(MARK(hd(cons(hd(tl(adx(y0))), y1)))) MARK(hd(hd(cons(hd(tl(zeros)), y0)))) -> c16(MARK(hd(cons(hd(tl(zeros)), y0)))) MARK(hd(hd(cons(hd(tl(incr(y0))), y1)))) -> c16(MARK(hd(cons(hd(tl(incr(y0))), y1)))) MARK(hd(hd(cons(hd(tl(hd(y0))), y1)))) -> c16(MARK(hd(cons(hd(tl(hd(y0))), y1)))) MARK(hd(hd(cons(hd(tl(tl(y0))), y1)))) -> c16(MARK(hd(cons(hd(tl(tl(y0))), y1)))) MARK(hd(hd(cons(hd(tl(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(hd(tl(cons(y0, y1))), y2)))) MARK(hd(hd(cons(hd(tl(y0)), y1)))) -> c16(MARK(hd(cons(hd(tl(y0)), y1)))) MARK(hd(hd(cons(hd(nats), y0)))) -> c16(MARK(hd(cons(hd(nats), y0)))) MARK(hd(hd(cons(tl(adx(nats)), y0)))) -> c16(MARK(hd(cons(tl(adx(nats)), y0)))) MARK(hd(hd(cons(tl(adx(adx(y0))), y1)))) -> c16(MARK(hd(cons(tl(adx(adx(y0))), y1)))) MARK(hd(hd(cons(tl(adx(zeros)), y0)))) -> c16(MARK(hd(cons(tl(adx(zeros)), y0)))) MARK(hd(hd(cons(tl(adx(incr(y0))), y1)))) -> c16(MARK(hd(cons(tl(adx(incr(y0))), y1)))) MARK(hd(hd(cons(tl(adx(hd(y0))), y1)))) -> c16(MARK(hd(cons(tl(adx(hd(y0))), y1)))) MARK(hd(hd(cons(tl(adx(tl(y0))), y1)))) -> c16(MARK(hd(cons(tl(adx(tl(y0))), y1)))) MARK(hd(hd(cons(tl(adx(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(tl(adx(cons(y0, y1))), y2)))) MARK(hd(hd(cons(tl(adx(0)), y0)))) -> c16(MARK(hd(cons(tl(adx(0)), y0)))) MARK(hd(hd(cons(tl(adx(s(y0))), y1)))) -> c16(MARK(hd(cons(tl(adx(s(y0))), y1)))) MARK(hd(hd(cons(tl(adx(y0)), y1)))) -> c16(MARK(hd(cons(tl(adx(y0)), y1)))) MARK(hd(hd(cons(tl(incr(nats)), y0)))) -> c16(MARK(hd(cons(tl(incr(nats)), y0)))) MARK(hd(hd(cons(tl(incr(adx(y0))), y1)))) -> c16(MARK(hd(cons(tl(incr(adx(y0))), y1)))) MARK(hd(hd(cons(tl(incr(zeros)), y0)))) -> c16(MARK(hd(cons(tl(incr(zeros)), y0)))) MARK(hd(hd(cons(tl(incr(incr(y0))), y1)))) -> c16(MARK(hd(cons(tl(incr(incr(y0))), y1)))) MARK(hd(hd(cons(tl(incr(hd(y0))), y1)))) -> c16(MARK(hd(cons(tl(incr(hd(y0))), y1)))) MARK(hd(hd(cons(tl(incr(tl(y0))), y1)))) -> c16(MARK(hd(cons(tl(incr(tl(y0))), y1)))) MARK(hd(hd(cons(tl(incr(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(tl(incr(cons(y0, y1))), y2)))) MARK(hd(hd(cons(tl(incr(0)), y0)))) -> c16(MARK(hd(cons(tl(incr(0)), y0)))) MARK(hd(hd(cons(tl(incr(s(y0))), y1)))) -> c16(MARK(hd(cons(tl(incr(s(y0))), y1)))) MARK(hd(hd(cons(tl(incr(y0)), y1)))) -> c16(MARK(hd(cons(tl(incr(y0)), y1)))) MARK(hd(hd(cons(tl(hd(nats)), y0)))) -> c16(MARK(hd(cons(tl(hd(nats)), y0)))) MARK(hd(hd(cons(tl(hd(adx(y0))), y1)))) -> c16(MARK(hd(cons(tl(hd(adx(y0))), y1)))) MARK(hd(hd(cons(tl(hd(zeros)), y0)))) -> c16(MARK(hd(cons(tl(hd(zeros)), y0)))) MARK(hd(hd(cons(tl(hd(incr(y0))), y1)))) -> c16(MARK(hd(cons(tl(hd(incr(y0))), y1)))) MARK(hd(hd(cons(tl(hd(hd(y0))), y1)))) -> c16(MARK(hd(cons(tl(hd(hd(y0))), y1)))) MARK(hd(hd(cons(tl(hd(tl(y0))), y1)))) -> c16(MARK(hd(cons(tl(hd(tl(y0))), y1)))) MARK(hd(hd(cons(tl(hd(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(tl(hd(cons(y0, y1))), y2)))) MARK(hd(hd(cons(tl(hd(y0)), y1)))) -> c16(MARK(hd(cons(tl(hd(y0)), y1)))) MARK(hd(hd(cons(tl(tl(nats)), y0)))) -> c16(MARK(hd(cons(tl(tl(nats)), y0)))) MARK(hd(hd(cons(tl(tl(adx(y0))), y1)))) -> c16(MARK(hd(cons(tl(tl(adx(y0))), y1)))) MARK(hd(hd(cons(tl(tl(zeros)), y0)))) -> c16(MARK(hd(cons(tl(tl(zeros)), y0)))) MARK(hd(hd(cons(tl(tl(incr(y0))), y1)))) -> c16(MARK(hd(cons(tl(tl(incr(y0))), y1)))) MARK(hd(hd(cons(tl(tl(hd(y0))), y1)))) -> c16(MARK(hd(cons(tl(tl(hd(y0))), y1)))) MARK(hd(hd(cons(tl(tl(tl(y0))), y1)))) -> c16(MARK(hd(cons(tl(tl(tl(y0))), y1)))) MARK(hd(hd(cons(tl(tl(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(tl(tl(cons(y0, y1))), y2)))) MARK(hd(hd(cons(tl(tl(y0)), y1)))) -> c16(MARK(hd(cons(tl(tl(y0)), y1)))) MARK(hd(hd(cons(tl(nats), y0)))) -> c16(MARK(hd(cons(tl(nats), y0)))) MARK(hd(hd(cons(hd(adx(0)), y0)))) -> c16(MARK(hd(cons(hd(adx(0)), y0)))) MARK(hd(hd(cons(hd(adx(s(y0))), y1)))) -> c16(MARK(hd(cons(hd(adx(s(y0))), y1)))) MARK(hd(hd(cons(hd(incr(0)), y0)))) -> c16(MARK(hd(cons(hd(incr(0)), y0)))) MARK(hd(hd(cons(hd(incr(s(y0))), y1)))) -> c16(MARK(hd(cons(hd(incr(s(y0))), y1)))) MARK(hd(hd(adx(hd(cons(y0, y1)))))) -> c16(MARK(hd(adx(hd(cons(y0, y1)))))) MARK(hd(hd(adx(tl(cons(y0, y1)))))) -> c16(MARK(hd(adx(tl(cons(y0, y1)))))) MARK(hd(hd(adx(hd(adx(nats)))))) -> c16(MARK(hd(adx(hd(adx(nats)))))) MARK(hd(hd(adx(hd(adx(adx(y0))))))) -> c16(MARK(hd(adx(hd(adx(adx(y0))))))) MARK(hd(hd(adx(hd(adx(zeros)))))) -> c16(MARK(hd(adx(hd(adx(zeros)))))) MARK(hd(hd(adx(hd(adx(incr(y0))))))) -> c16(MARK(hd(adx(hd(adx(incr(y0))))))) MARK(hd(hd(adx(hd(adx(hd(y0))))))) -> c16(MARK(hd(adx(hd(adx(hd(y0))))))) MARK(hd(hd(adx(hd(adx(tl(y0))))))) -> c16(MARK(hd(adx(hd(adx(tl(y0))))))) MARK(hd(hd(adx(hd(adx(cons(y0, y1))))))) -> c16(MARK(hd(adx(hd(adx(cons(y0, y1))))))) MARK(hd(hd(adx(hd(adx(y0)))))) -> c16(MARK(hd(adx(hd(adx(y0)))))) MARK(hd(hd(adx(hd(incr(nats)))))) -> c16(MARK(hd(adx(hd(incr(nats)))))) MARK(hd(hd(adx(hd(incr(adx(y0))))))) -> c16(MARK(hd(adx(hd(incr(adx(y0))))))) MARK(hd(hd(adx(hd(incr(zeros)))))) -> c16(MARK(hd(adx(hd(incr(zeros)))))) MARK(hd(hd(adx(hd(incr(incr(y0))))))) -> c16(MARK(hd(adx(hd(incr(incr(y0))))))) MARK(hd(hd(adx(hd(incr(hd(y0))))))) -> c16(MARK(hd(adx(hd(incr(hd(y0))))))) MARK(hd(hd(adx(hd(incr(tl(y0))))))) -> c16(MARK(hd(adx(hd(incr(tl(y0))))))) MARK(hd(hd(adx(hd(incr(cons(y0, y1))))))) -> c16(MARK(hd(adx(hd(incr(cons(y0, y1))))))) MARK(hd(hd(adx(hd(incr(y0)))))) -> c16(MARK(hd(adx(hd(incr(y0)))))) MARK(hd(hd(adx(hd(hd(nats)))))) -> c16(MARK(hd(adx(hd(hd(nats)))))) MARK(hd(hd(adx(hd(hd(adx(y0))))))) -> c16(MARK(hd(adx(hd(hd(adx(y0))))))) MARK(hd(hd(adx(hd(hd(incr(y0))))))) -> c16(MARK(hd(adx(hd(hd(incr(y0))))))) MARK(hd(hd(adx(hd(hd(hd(y0))))))) -> c16(MARK(hd(adx(hd(hd(hd(y0))))))) MARK(hd(hd(adx(hd(hd(tl(y0))))))) -> c16(MARK(hd(adx(hd(hd(tl(y0))))))) MARK(hd(hd(adx(hd(hd(cons(y0, y1))))))) -> c16(MARK(hd(adx(hd(hd(cons(y0, y1))))))) MARK(hd(hd(adx(hd(hd(y0)))))) -> c16(MARK(hd(adx(hd(hd(y0)))))) MARK(hd(hd(adx(hd(tl(nats)))))) -> c16(MARK(hd(adx(hd(tl(nats)))))) MARK(hd(hd(adx(hd(tl(adx(y0))))))) -> c16(MARK(hd(adx(hd(tl(adx(y0))))))) MARK(hd(hd(adx(hd(tl(incr(y0))))))) -> c16(MARK(hd(adx(hd(tl(incr(y0))))))) MARK(hd(hd(adx(hd(tl(hd(y0))))))) -> c16(MARK(hd(adx(hd(tl(hd(y0))))))) MARK(hd(hd(adx(hd(tl(tl(y0))))))) -> c16(MARK(hd(adx(hd(tl(tl(y0))))))) MARK(hd(hd(adx(hd(tl(cons(y0, y1))))))) -> c16(MARK(hd(adx(hd(tl(cons(y0, y1))))))) MARK(hd(hd(adx(hd(tl(y0)))))) -> c16(MARK(hd(adx(hd(tl(y0)))))) MARK(hd(hd(adx(hd(nats))))) -> c16(MARK(hd(adx(hd(nats))))) MARK(hd(hd(adx(tl(adx(nats)))))) -> c16(MARK(hd(adx(tl(adx(nats)))))) MARK(hd(hd(adx(tl(adx(adx(y0))))))) -> c16(MARK(hd(adx(tl(adx(adx(y0))))))) MARK(hd(hd(adx(tl(adx(zeros)))))) -> c16(MARK(hd(adx(tl(adx(zeros)))))) MARK(hd(hd(adx(tl(adx(incr(y0))))))) -> c16(MARK(hd(adx(tl(adx(incr(y0))))))) MARK(hd(hd(adx(tl(adx(hd(y0))))))) -> c16(MARK(hd(adx(tl(adx(hd(y0))))))) MARK(hd(hd(adx(tl(adx(tl(y0))))))) -> c16(MARK(hd(adx(tl(adx(tl(y0))))))) MARK(hd(hd(adx(tl(adx(cons(y0, y1))))))) -> c16(MARK(hd(adx(tl(adx(cons(y0, y1))))))) MARK(hd(hd(adx(tl(adx(y0)))))) -> c16(MARK(hd(adx(tl(adx(y0)))))) MARK(hd(hd(adx(tl(incr(nats)))))) -> c16(MARK(hd(adx(tl(incr(nats)))))) MARK(hd(hd(adx(tl(incr(adx(y0))))))) -> c16(MARK(hd(adx(tl(incr(adx(y0))))))) MARK(hd(hd(adx(tl(incr(zeros)))))) -> c16(MARK(hd(adx(tl(incr(zeros)))))) MARK(hd(hd(adx(tl(incr(incr(y0))))))) -> c16(MARK(hd(adx(tl(incr(incr(y0))))))) MARK(hd(hd(adx(tl(incr(hd(y0))))))) -> c16(MARK(hd(adx(tl(incr(hd(y0))))))) MARK(hd(hd(adx(tl(incr(tl(y0))))))) -> c16(MARK(hd(adx(tl(incr(tl(y0))))))) MARK(hd(hd(adx(tl(incr(cons(y0, y1))))))) -> c16(MARK(hd(adx(tl(incr(cons(y0, y1))))))) MARK(hd(hd(adx(tl(incr(s(y0))))))) -> c16(MARK(hd(adx(tl(incr(s(y0))))))) MARK(hd(hd(adx(tl(incr(y0)))))) -> c16(MARK(hd(adx(tl(incr(y0)))))) MARK(hd(hd(adx(tl(hd(nats)))))) -> c16(MARK(hd(adx(tl(hd(nats)))))) MARK(hd(hd(adx(tl(hd(adx(y0))))))) -> c16(MARK(hd(adx(tl(hd(adx(y0))))))) MARK(hd(hd(adx(tl(hd(incr(y0))))))) -> c16(MARK(hd(adx(tl(hd(incr(y0))))))) MARK(hd(hd(adx(tl(hd(hd(y0))))))) -> c16(MARK(hd(adx(tl(hd(hd(y0))))))) MARK(hd(hd(adx(tl(hd(tl(y0))))))) -> c16(MARK(hd(adx(tl(hd(tl(y0))))))) MARK(hd(hd(adx(tl(hd(cons(y0, y1))))))) -> c16(MARK(hd(adx(tl(hd(cons(y0, y1))))))) MARK(hd(hd(adx(tl(hd(y0)))))) -> c16(MARK(hd(adx(tl(hd(y0)))))) MARK(hd(hd(adx(tl(tl(nats)))))) -> c16(MARK(hd(adx(tl(tl(nats)))))) MARK(hd(hd(adx(tl(tl(adx(y0))))))) -> c16(MARK(hd(adx(tl(tl(adx(y0))))))) MARK(hd(hd(adx(tl(tl(incr(y0))))))) -> c16(MARK(hd(adx(tl(tl(incr(y0))))))) MARK(hd(hd(adx(tl(tl(hd(y0))))))) -> c16(MARK(hd(adx(tl(tl(hd(y0))))))) MARK(hd(hd(adx(tl(tl(tl(y0))))))) -> c16(MARK(hd(adx(tl(tl(tl(y0))))))) MARK(hd(hd(adx(tl(tl(cons(y0, y1))))))) -> c16(MARK(hd(adx(tl(tl(cons(y0, y1))))))) MARK(hd(hd(adx(tl(tl(y0)))))) -> c16(MARK(hd(adx(tl(tl(y0)))))) MARK(hd(hd(adx(tl(nats))))) -> c16(MARK(hd(adx(tl(nats))))) MARK(hd(hd(adx(hd(adx(0)))))) -> c16(MARK(hd(adx(hd(adx(0)))))) MARK(hd(hd(adx(hd(adx(s(y0))))))) -> c16(MARK(hd(adx(hd(adx(s(y0))))))) MARK(hd(hd(adx(hd(incr(0)))))) -> c16(MARK(hd(adx(hd(incr(0)))))) MARK(hd(hd(adx(hd(incr(s(y0))))))) -> c16(MARK(hd(adx(hd(incr(s(y0))))))) MARK(hd(hd(adx(hd(hd(zeros)))))) -> c16(MARK(hd(adx(hd(hd(zeros)))))) MARK(hd(hd(adx(tl(hd(zeros)))))) -> c16(MARK(hd(adx(tl(hd(zeros)))))) MARK(hd(hd(adx(tl(adx(0)))))) -> c16(MARK(hd(adx(tl(adx(0)))))) MARK(hd(hd(adx(hd(tl(zeros)))))) -> c16(MARK(hd(adx(hd(tl(zeros)))))) MARK(hd(hd(adx(tl(tl(zeros)))))) -> c16(MARK(hd(adx(tl(tl(zeros)))))) MARK(hd(hd(adx(tl(adx(s(y0))))))) -> c16(MARK(hd(adx(tl(adx(s(y0))))))) MARK(hd(hd(adx(tl(incr(0)))))) -> c16(MARK(hd(adx(tl(incr(0)))))) MARK(hd(hd(incr(hd(cons(y0, y1)))))) -> c16(MARK(hd(incr(hd(cons(y0, y1)))))) MARK(hd(hd(incr(tl(cons(y0, y1)))))) -> c16(MARK(hd(incr(tl(cons(y0, y1)))))) MARK(hd(hd(incr(hd(adx(adx(y0))))))) -> c16(MARK(hd(incr(hd(adx(adx(y0))))))) MARK(hd(hd(incr(hd(adx(incr(y0))))))) -> c16(MARK(hd(incr(hd(adx(incr(y0))))))) MARK(hd(hd(incr(hd(adx(hd(y0))))))) -> c16(MARK(hd(incr(hd(adx(hd(y0))))))) MARK(hd(hd(incr(hd(adx(tl(y0))))))) -> c16(MARK(hd(incr(hd(adx(tl(y0))))))) MARK(hd(hd(incr(hd(adx(y0)))))) -> c16(MARK(hd(incr(hd(adx(y0)))))) MARK(hd(hd(incr(hd(incr(nats)))))) -> c16(MARK(hd(incr(hd(incr(nats)))))) MARK(hd(hd(incr(hd(incr(adx(y0))))))) -> c16(MARK(hd(incr(hd(incr(adx(y0))))))) MARK(hd(hd(incr(hd(incr(zeros)))))) -> c16(MARK(hd(incr(hd(incr(zeros)))))) MARK(hd(hd(incr(hd(incr(incr(y0))))))) -> c16(MARK(hd(incr(hd(incr(incr(y0))))))) MARK(hd(hd(incr(hd(incr(hd(y0))))))) -> c16(MARK(hd(incr(hd(incr(hd(y0))))))) MARK(hd(hd(incr(hd(incr(tl(y0))))))) -> c16(MARK(hd(incr(hd(incr(tl(y0))))))) MARK(hd(hd(incr(hd(incr(cons(y0, y1))))))) -> c16(MARK(hd(incr(hd(incr(cons(y0, y1))))))) MARK(hd(hd(incr(hd(incr(y0)))))) -> c16(MARK(hd(incr(hd(incr(y0)))))) MARK(hd(hd(incr(hd(hd(nats)))))) -> c16(MARK(hd(incr(hd(hd(nats)))))) MARK(hd(hd(incr(hd(hd(adx(y0))))))) -> c16(MARK(hd(incr(hd(hd(adx(y0))))))) MARK(hd(hd(incr(hd(hd(incr(y0))))))) -> c16(MARK(hd(incr(hd(hd(incr(y0))))))) MARK(hd(hd(incr(hd(hd(hd(y0))))))) -> c16(MARK(hd(incr(hd(hd(hd(y0))))))) MARK(hd(hd(incr(hd(hd(tl(y0))))))) -> c16(MARK(hd(incr(hd(hd(tl(y0))))))) MARK(hd(hd(incr(hd(hd(cons(y0, y1))))))) -> c16(MARK(hd(incr(hd(hd(cons(y0, y1))))))) MARK(hd(hd(incr(hd(hd(y0)))))) -> c16(MARK(hd(incr(hd(hd(y0)))))) MARK(hd(hd(incr(hd(tl(nats)))))) -> c16(MARK(hd(incr(hd(tl(nats)))))) MARK(hd(hd(incr(hd(tl(adx(y0))))))) -> c16(MARK(hd(incr(hd(tl(adx(y0))))))) MARK(hd(hd(incr(hd(tl(incr(y0))))))) -> c16(MARK(hd(incr(hd(tl(incr(y0))))))) MARK(hd(hd(incr(hd(tl(hd(y0))))))) -> c16(MARK(hd(incr(hd(tl(hd(y0))))))) MARK(hd(hd(incr(hd(tl(tl(y0))))))) -> c16(MARK(hd(incr(hd(tl(tl(y0))))))) MARK(hd(hd(incr(hd(tl(cons(y0, y1))))))) -> c16(MARK(hd(incr(hd(tl(cons(y0, y1))))))) MARK(hd(hd(incr(hd(tl(y0)))))) -> c16(MARK(hd(incr(hd(tl(y0)))))) MARK(hd(hd(incr(hd(nats))))) -> c16(MARK(hd(incr(hd(nats))))) MARK(hd(hd(incr(tl(adx(adx(y0))))))) -> c16(MARK(hd(incr(tl(adx(adx(y0))))))) MARK(hd(hd(incr(tl(adx(incr(y0))))))) -> c16(MARK(hd(incr(tl(adx(incr(y0))))))) MARK(hd(hd(incr(tl(adx(hd(y0))))))) -> c16(MARK(hd(incr(tl(adx(hd(y0))))))) MARK(hd(hd(incr(tl(adx(tl(y0))))))) -> c16(MARK(hd(incr(tl(adx(tl(y0))))))) MARK(hd(hd(incr(tl(adx(y0)))))) -> c16(MARK(hd(incr(tl(adx(y0)))))) MARK(hd(hd(incr(tl(incr(nats)))))) -> c16(MARK(hd(incr(tl(incr(nats)))))) MARK(hd(hd(incr(tl(incr(adx(y0))))))) -> c16(MARK(hd(incr(tl(incr(adx(y0))))))) MARK(hd(hd(incr(tl(incr(zeros)))))) -> c16(MARK(hd(incr(tl(incr(zeros)))))) MARK(hd(hd(incr(tl(incr(incr(y0))))))) -> c16(MARK(hd(incr(tl(incr(incr(y0))))))) MARK(hd(hd(incr(tl(incr(hd(y0))))))) -> c16(MARK(hd(incr(tl(incr(hd(y0))))))) MARK(hd(hd(incr(tl(incr(tl(y0))))))) -> c16(MARK(hd(incr(tl(incr(tl(y0))))))) MARK(hd(hd(incr(tl(incr(cons(y0, y1))))))) -> c16(MARK(hd(incr(tl(incr(cons(y0, y1))))))) MARK(hd(hd(incr(tl(incr(y0)))))) -> c16(MARK(hd(incr(tl(incr(y0)))))) MARK(hd(hd(incr(tl(hd(nats)))))) -> c16(MARK(hd(incr(tl(hd(nats)))))) MARK(hd(hd(incr(tl(hd(adx(y0))))))) -> c16(MARK(hd(incr(tl(hd(adx(y0))))))) MARK(hd(hd(incr(tl(hd(incr(y0))))))) -> c16(MARK(hd(incr(tl(hd(incr(y0))))))) MARK(hd(hd(incr(tl(hd(hd(y0))))))) -> c16(MARK(hd(incr(tl(hd(hd(y0))))))) MARK(hd(hd(incr(tl(hd(tl(y0))))))) -> c16(MARK(hd(incr(tl(hd(tl(y0))))))) MARK(hd(hd(incr(tl(hd(cons(y0, y1))))))) -> c16(MARK(hd(incr(tl(hd(cons(y0, y1))))))) MARK(hd(hd(incr(tl(hd(y0)))))) -> c16(MARK(hd(incr(tl(hd(y0)))))) MARK(hd(hd(incr(tl(tl(nats)))))) -> c16(MARK(hd(incr(tl(tl(nats)))))) MARK(hd(hd(incr(tl(tl(adx(y0))))))) -> c16(MARK(hd(incr(tl(tl(adx(y0))))))) MARK(hd(hd(incr(tl(tl(incr(y0))))))) -> c16(MARK(hd(incr(tl(tl(incr(y0))))))) MARK(hd(hd(incr(tl(tl(hd(y0))))))) -> c16(MARK(hd(incr(tl(tl(hd(y0))))))) MARK(hd(hd(incr(tl(tl(tl(y0))))))) -> c16(MARK(hd(incr(tl(tl(tl(y0))))))) MARK(hd(hd(incr(tl(tl(cons(y0, y1))))))) -> c16(MARK(hd(incr(tl(tl(cons(y0, y1))))))) MARK(hd(hd(incr(tl(tl(y0)))))) -> c16(MARK(hd(incr(tl(tl(y0)))))) MARK(hd(hd(incr(tl(nats))))) -> c16(MARK(hd(incr(tl(nats))))) MARK(hd(hd(incr(hd(incr(0)))))) -> c16(MARK(hd(incr(hd(incr(0)))))) MARK(hd(hd(incr(hd(incr(s(y0))))))) -> c16(MARK(hd(incr(hd(incr(s(y0))))))) MARK(hd(hd(incr(hd(hd(zeros)))))) -> c16(MARK(hd(incr(hd(hd(zeros)))))) MARK(hd(hd(incr(tl(hd(zeros)))))) -> c16(MARK(hd(incr(tl(hd(zeros)))))) MARK(hd(hd(incr(hd(tl(zeros)))))) -> c16(MARK(hd(incr(hd(tl(zeros)))))) MARK(hd(hd(incr(tl(tl(zeros)))))) -> c16(MARK(hd(incr(tl(tl(zeros)))))) MARK(hd(hd(incr(tl(incr(0)))))) -> c16(MARK(hd(incr(tl(incr(0)))))) MARK(hd(hd(incr(adx(adx(y0)))))) -> c16(MARK(hd(incr(adx(adx(y0)))))) MARK(hd(hd(incr(adx(incr(y0)))))) -> c16(MARK(hd(incr(adx(incr(y0)))))) MARK(hd(hd(incr(adx(hd(cons(y0, y1))))))) -> c16(MARK(hd(incr(adx(hd(cons(y0, y1))))))) MARK(hd(hd(incr(adx(tl(cons(y0, y1))))))) -> c16(MARK(hd(incr(adx(tl(cons(y0, y1))))))) MARK(hd(hd(incr(adx(hd(adx(nats))))))) -> c16(MARK(hd(incr(adx(hd(adx(nats))))))) MARK(hd(hd(incr(adx(hd(adx(adx(y0)))))))) -> c16(MARK(hd(incr(adx(hd(adx(adx(y0)))))))) MARK(hd(hd(incr(adx(hd(adx(zeros))))))) -> c16(MARK(hd(incr(adx(hd(adx(zeros))))))) MARK(hd(hd(incr(adx(hd(adx(incr(y0)))))))) -> c16(MARK(hd(incr(adx(hd(adx(incr(y0)))))))) MARK(hd(hd(incr(adx(hd(adx(hd(y0)))))))) -> c16(MARK(hd(incr(adx(hd(adx(hd(y0)))))))) MARK(hd(hd(incr(adx(hd(adx(tl(y0)))))))) -> c16(MARK(hd(incr(adx(hd(adx(tl(y0)))))))) MARK(hd(hd(incr(adx(hd(adx(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(hd(adx(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(hd(adx(y0))))))) -> c16(MARK(hd(incr(adx(hd(adx(y0))))))) MARK(hd(hd(incr(adx(hd(incr(nats))))))) -> c16(MARK(hd(incr(adx(hd(incr(nats))))))) MARK(hd(hd(incr(adx(hd(incr(adx(y0)))))))) -> c16(MARK(hd(incr(adx(hd(incr(adx(y0)))))))) MARK(hd(hd(incr(adx(hd(incr(zeros))))))) -> c16(MARK(hd(incr(adx(hd(incr(zeros))))))) MARK(hd(hd(incr(adx(hd(incr(incr(y0)))))))) -> c16(MARK(hd(incr(adx(hd(incr(incr(y0)))))))) MARK(hd(hd(incr(adx(hd(incr(hd(y0)))))))) -> c16(MARK(hd(incr(adx(hd(incr(hd(y0)))))))) MARK(hd(hd(incr(adx(hd(incr(tl(y0)))))))) -> c16(MARK(hd(incr(adx(hd(incr(tl(y0)))))))) MARK(hd(hd(incr(adx(hd(incr(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(hd(incr(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(hd(incr(y0))))))) -> c16(MARK(hd(incr(adx(hd(incr(y0))))))) MARK(hd(hd(incr(adx(hd(hd(nats))))))) -> c16(MARK(hd(incr(adx(hd(hd(nats))))))) MARK(hd(hd(incr(adx(hd(hd(adx(y0)))))))) -> c16(MARK(hd(incr(adx(hd(hd(adx(y0)))))))) MARK(hd(hd(incr(adx(hd(hd(incr(y0)))))))) -> c16(MARK(hd(incr(adx(hd(hd(incr(y0)))))))) MARK(hd(hd(incr(adx(hd(hd(hd(y0)))))))) -> c16(MARK(hd(incr(adx(hd(hd(hd(y0)))))))) MARK(hd(hd(incr(adx(hd(hd(tl(y0)))))))) -> c16(MARK(hd(incr(adx(hd(hd(tl(y0)))))))) MARK(hd(hd(incr(adx(hd(hd(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(hd(hd(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(hd(hd(y0))))))) -> c16(MARK(hd(incr(adx(hd(hd(y0))))))) MARK(hd(hd(incr(adx(hd(tl(nats))))))) -> c16(MARK(hd(incr(adx(hd(tl(nats))))))) MARK(hd(hd(incr(adx(hd(tl(adx(y0)))))))) -> c16(MARK(hd(incr(adx(hd(tl(adx(y0)))))))) MARK(hd(hd(incr(adx(hd(tl(incr(y0)))))))) -> c16(MARK(hd(incr(adx(hd(tl(incr(y0)))))))) MARK(hd(hd(incr(adx(hd(tl(hd(y0)))))))) -> c16(MARK(hd(incr(adx(hd(tl(hd(y0)))))))) MARK(hd(hd(incr(adx(hd(tl(tl(y0)))))))) -> c16(MARK(hd(incr(adx(hd(tl(tl(y0)))))))) MARK(hd(hd(incr(adx(hd(tl(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(hd(tl(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(hd(tl(y0))))))) -> c16(MARK(hd(incr(adx(hd(tl(y0))))))) MARK(hd(hd(incr(adx(hd(nats)))))) -> c16(MARK(hd(incr(adx(hd(nats)))))) MARK(hd(hd(incr(adx(tl(adx(nats))))))) -> c16(MARK(hd(incr(adx(tl(adx(nats))))))) MARK(hd(hd(incr(adx(tl(adx(adx(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(adx(y0)))))))) MARK(hd(hd(incr(adx(tl(adx(zeros))))))) -> c16(MARK(hd(incr(adx(tl(adx(zeros))))))) MARK(hd(hd(incr(adx(tl(adx(incr(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(incr(y0)))))))) MARK(hd(hd(incr(adx(tl(adx(hd(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(hd(y0)))))))) MARK(hd(hd(incr(adx(tl(adx(tl(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(tl(y0)))))))) MARK(hd(hd(incr(adx(tl(adx(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(tl(adx(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(tl(adx(y0))))))) -> c16(MARK(hd(incr(adx(tl(adx(y0))))))) MARK(hd(hd(incr(adx(tl(incr(nats))))))) -> c16(MARK(hd(incr(adx(tl(incr(nats))))))) MARK(hd(hd(incr(adx(tl(incr(adx(y0)))))))) -> c16(MARK(hd(incr(adx(tl(incr(adx(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(zeros))))))) -> c16(MARK(hd(incr(adx(tl(incr(zeros))))))) MARK(hd(hd(incr(adx(tl(incr(incr(y0)))))))) -> c16(MARK(hd(incr(adx(tl(incr(incr(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(hd(y0)))))))) -> c16(MARK(hd(incr(adx(tl(incr(hd(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(tl(y0)))))))) -> c16(MARK(hd(incr(adx(tl(incr(tl(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(tl(incr(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(tl(incr(s(y0)))))))) -> c16(MARK(hd(incr(adx(tl(incr(s(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(y0))))))) -> c16(MARK(hd(incr(adx(tl(incr(y0))))))) MARK(hd(hd(incr(adx(tl(hd(nats))))))) -> c16(MARK(hd(incr(adx(tl(hd(nats))))))) MARK(hd(hd(incr(adx(tl(hd(adx(y0)))))))) -> c16(MARK(hd(incr(adx(tl(hd(adx(y0)))))))) MARK(hd(hd(incr(adx(tl(hd(incr(y0)))))))) -> c16(MARK(hd(incr(adx(tl(hd(incr(y0)))))))) MARK(hd(hd(incr(adx(tl(hd(hd(y0)))))))) -> c16(MARK(hd(incr(adx(tl(hd(hd(y0)))))))) MARK(hd(hd(incr(adx(tl(hd(tl(y0)))))))) -> c16(MARK(hd(incr(adx(tl(hd(tl(y0)))))))) MARK(hd(hd(incr(adx(tl(hd(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(tl(hd(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(tl(hd(y0))))))) -> c16(MARK(hd(incr(adx(tl(hd(y0))))))) MARK(hd(hd(incr(adx(tl(tl(nats))))))) -> c16(MARK(hd(incr(adx(tl(tl(nats))))))) MARK(hd(hd(incr(adx(tl(tl(adx(y0)))))))) -> c16(MARK(hd(incr(adx(tl(tl(adx(y0)))))))) MARK(hd(hd(incr(adx(tl(tl(incr(y0)))))))) -> c16(MARK(hd(incr(adx(tl(tl(incr(y0)))))))) MARK(hd(hd(incr(adx(tl(tl(hd(y0)))))))) -> c16(MARK(hd(incr(adx(tl(tl(hd(y0)))))))) MARK(hd(hd(incr(adx(tl(tl(tl(y0)))))))) -> c16(MARK(hd(incr(adx(tl(tl(tl(y0)))))))) MARK(hd(hd(incr(adx(tl(tl(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(tl(tl(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(tl(tl(y0))))))) -> c16(MARK(hd(incr(adx(tl(tl(y0))))))) MARK(hd(hd(incr(adx(tl(nats)))))) -> c16(MARK(hd(incr(adx(tl(nats)))))) MARK(hd(hd(incr(adx(hd(adx(0))))))) -> c16(MARK(hd(incr(adx(hd(adx(0))))))) MARK(hd(hd(incr(adx(hd(adx(s(y0)))))))) -> c16(MARK(hd(incr(adx(hd(adx(s(y0)))))))) MARK(hd(hd(incr(adx(hd(incr(0))))))) -> c16(MARK(hd(incr(adx(hd(incr(0))))))) MARK(hd(hd(incr(adx(hd(incr(s(y0)))))))) -> c16(MARK(hd(incr(adx(hd(incr(s(y0)))))))) MARK(hd(hd(incr(adx(hd(hd(zeros))))))) -> c16(MARK(hd(incr(adx(hd(hd(zeros))))))) MARK(hd(hd(incr(adx(tl(hd(zeros))))))) -> c16(MARK(hd(incr(adx(tl(hd(zeros))))))) MARK(hd(hd(incr(adx(tl(adx(0))))))) -> c16(MARK(hd(incr(adx(tl(adx(0))))))) MARK(hd(hd(incr(adx(hd(tl(zeros))))))) -> c16(MARK(hd(incr(adx(hd(tl(zeros))))))) MARK(hd(hd(incr(adx(tl(tl(zeros))))))) -> c16(MARK(hd(incr(adx(tl(tl(zeros))))))) MARK(hd(hd(incr(adx(tl(adx(s(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(s(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(0))))))) -> c16(MARK(hd(incr(adx(tl(incr(0))))))) MARK(hd(hd(incr(hd(adx(nats)))))) -> c16(MARK(hd(incr(hd(adx(nats)))))) MARK(hd(hd(incr(hd(adx(zeros)))))) -> c16(MARK(hd(incr(hd(adx(zeros)))))) MARK(hd(hd(incr(hd(adx(cons(y0, y1))))))) -> c16(MARK(hd(incr(hd(adx(cons(y0, y1))))))) MARK(hd(hd(incr(tl(adx(nats)))))) -> c16(MARK(hd(incr(tl(adx(nats)))))) MARK(hd(hd(incr(tl(adx(zeros)))))) -> c16(MARK(hd(incr(tl(adx(zeros)))))) MARK(hd(hd(incr(tl(adx(cons(y0, y1))))))) -> c16(MARK(hd(incr(tl(adx(cons(y0, y1))))))) MARK(hd(hd(incr(tl(incr(s(y0))))))) -> c16(MARK(hd(incr(tl(incr(s(y0))))))) ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__nats -> a__adx(a__zeros) a__nats -> nats a__zeros -> cons(0, zeros) a__zeros -> zeros a__incr(cons(z0, z1)) -> cons(s(z0), incr(z1)) a__incr(z0) -> incr(z0) a__adx(cons(z0, z1)) -> a__incr(cons(z0, adx(z1))) a__adx(z0) -> adx(z0) a__hd(cons(z0, z1)) -> mark(z0) a__hd(z0) -> hd(z0) a__tl(cons(z0, z1)) -> mark(z1) a__tl(z0) -> tl(z0) mark(nats) -> a__nats mark(adx(z0)) -> a__adx(mark(z0)) mark(zeros) -> a__zeros mark(incr(z0)) -> a__incr(mark(z0)) mark(hd(z0)) -> a__hd(mark(z0)) mark(tl(z0)) -> a__tl(mark(z0)) mark(cons(z0, z1)) -> cons(z0, z1) mark(0) -> 0 mark(s(z0)) -> s(z0) Tuples: MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) MARK(tl(nats)) -> c17(A__TL(a__adx(a__zeros))) A__HD(cons(adx(y0), z1)) -> c8(MARK(adx(y0))) A__HD(cons(incr(y0), z1)) -> c8(MARK(incr(y0))) A__HD(cons(hd(cons(y0, y1)), z1)) -> c8(MARK(hd(cons(y0, y1)))) A__HD(cons(tl(cons(y0, y1)), z1)) -> c8(MARK(tl(cons(y0, y1)))) A__HD(cons(hd(adx(nats)), z1)) -> c8(MARK(hd(adx(nats)))) A__HD(cons(hd(adx(adx(y0))), z1)) -> c8(MARK(hd(adx(adx(y0))))) A__HD(cons(hd(adx(zeros)), z1)) -> c8(MARK(hd(adx(zeros)))) A__HD(cons(hd(adx(incr(y0))), z1)) -> c8(MARK(hd(adx(incr(y0))))) A__HD(cons(hd(adx(hd(y0))), z1)) -> c8(MARK(hd(adx(hd(y0))))) A__HD(cons(hd(adx(tl(y0))), z1)) -> c8(MARK(hd(adx(tl(y0))))) A__HD(cons(hd(adx(cons(y0, y1))), z1)) -> c8(MARK(hd(adx(cons(y0, y1))))) A__HD(cons(hd(adx(y0)), z1)) -> c8(MARK(hd(adx(y0)))) A__HD(cons(hd(incr(nats)), z1)) -> c8(MARK(hd(incr(nats)))) A__HD(cons(hd(incr(adx(y0))), z1)) -> c8(MARK(hd(incr(adx(y0))))) A__HD(cons(hd(incr(zeros)), z1)) -> c8(MARK(hd(incr(zeros)))) A__HD(cons(hd(incr(incr(y0))), z1)) -> c8(MARK(hd(incr(incr(y0))))) A__HD(cons(hd(incr(hd(y0))), z1)) -> c8(MARK(hd(incr(hd(y0))))) A__HD(cons(hd(incr(tl(y0))), z1)) -> c8(MARK(hd(incr(tl(y0))))) A__HD(cons(hd(incr(y0)), z1)) -> c8(MARK(hd(incr(y0)))) A__HD(cons(hd(hd(nats)), z1)) -> c8(MARK(hd(hd(nats)))) A__HD(cons(hd(hd(adx(y0))), z1)) -> c8(MARK(hd(hd(adx(y0))))) A__HD(cons(hd(hd(zeros)), z1)) -> c8(MARK(hd(hd(zeros)))) A__HD(cons(hd(hd(incr(y0))), z1)) -> c8(MARK(hd(hd(incr(y0))))) A__HD(cons(hd(hd(hd(y0))), z1)) -> c8(MARK(hd(hd(hd(y0))))) A__HD(cons(hd(hd(tl(y0))), z1)) -> c8(MARK(hd(hd(tl(y0))))) A__HD(cons(hd(hd(cons(y0, y1))), z1)) -> c8(MARK(hd(hd(cons(y0, y1))))) A__HD(cons(hd(hd(y0)), z1)) -> c8(MARK(hd(hd(y0)))) A__HD(cons(hd(tl(nats)), z1)) -> c8(MARK(hd(tl(nats)))) A__HD(cons(hd(tl(adx(y0))), z1)) -> c8(MARK(hd(tl(adx(y0))))) A__HD(cons(hd(tl(zeros)), z1)) -> c8(MARK(hd(tl(zeros)))) A__HD(cons(hd(tl(incr(y0))), z1)) -> c8(MARK(hd(tl(incr(y0))))) A__HD(cons(hd(tl(hd(y0))), z1)) -> c8(MARK(hd(tl(hd(y0))))) A__HD(cons(hd(tl(tl(y0))), z1)) -> c8(MARK(hd(tl(tl(y0))))) A__HD(cons(hd(tl(cons(y0, y1))), z1)) -> c8(MARK(hd(tl(cons(y0, y1))))) A__HD(cons(hd(tl(y0)), z1)) -> c8(MARK(hd(tl(y0)))) A__HD(cons(hd(nats), z1)) -> c8(MARK(hd(nats))) A__HD(cons(tl(adx(nats)), z1)) -> c8(MARK(tl(adx(nats)))) A__HD(cons(tl(adx(adx(y0))), z1)) -> c8(MARK(tl(adx(adx(y0))))) A__HD(cons(tl(adx(zeros)), z1)) -> c8(MARK(tl(adx(zeros)))) A__HD(cons(tl(adx(incr(y0))), z1)) -> c8(MARK(tl(adx(incr(y0))))) A__HD(cons(tl(adx(hd(y0))), z1)) -> c8(MARK(tl(adx(hd(y0))))) A__HD(cons(tl(adx(tl(y0))), z1)) -> c8(MARK(tl(adx(tl(y0))))) A__HD(cons(tl(adx(cons(y0, y1))), z1)) -> c8(MARK(tl(adx(cons(y0, y1))))) A__HD(cons(tl(adx(0)), z1)) -> c8(MARK(tl(adx(0)))) A__HD(cons(tl(adx(s(y0))), z1)) -> c8(MARK(tl(adx(s(y0))))) A__HD(cons(tl(adx(y0)), z1)) -> c8(MARK(tl(adx(y0)))) A__HD(cons(tl(incr(nats)), z1)) -> c8(MARK(tl(incr(nats)))) A__HD(cons(tl(incr(adx(y0))), z1)) -> c8(MARK(tl(incr(adx(y0))))) A__HD(cons(tl(incr(zeros)), z1)) -> c8(MARK(tl(incr(zeros)))) A__HD(cons(tl(incr(incr(y0))), z1)) -> c8(MARK(tl(incr(incr(y0))))) A__HD(cons(tl(incr(hd(y0))), z1)) -> c8(MARK(tl(incr(hd(y0))))) A__HD(cons(tl(incr(tl(y0))), z1)) -> c8(MARK(tl(incr(tl(y0))))) A__HD(cons(tl(incr(cons(y0, y1))), z1)) -> c8(MARK(tl(incr(cons(y0, y1))))) A__HD(cons(tl(incr(0)), z1)) -> c8(MARK(tl(incr(0)))) A__HD(cons(tl(incr(s(y0))), z1)) -> c8(MARK(tl(incr(s(y0))))) A__HD(cons(tl(incr(y0)), z1)) -> c8(MARK(tl(incr(y0)))) A__HD(cons(tl(hd(nats)), z1)) -> c8(MARK(tl(hd(nats)))) A__HD(cons(tl(hd(adx(y0))), z1)) -> c8(MARK(tl(hd(adx(y0))))) A__HD(cons(tl(hd(zeros)), z1)) -> c8(MARK(tl(hd(zeros)))) A__HD(cons(tl(hd(incr(y0))), z1)) -> c8(MARK(tl(hd(incr(y0))))) A__HD(cons(tl(hd(hd(y0))), z1)) -> c8(MARK(tl(hd(hd(y0))))) A__HD(cons(tl(hd(tl(y0))), z1)) -> c8(MARK(tl(hd(tl(y0))))) A__HD(cons(tl(hd(cons(y0, y1))), z1)) -> c8(MARK(tl(hd(cons(y0, y1))))) A__HD(cons(tl(hd(y0)), z1)) -> c8(MARK(tl(hd(y0)))) A__HD(cons(tl(tl(nats)), z1)) -> c8(MARK(tl(tl(nats)))) A__HD(cons(tl(tl(adx(y0))), z1)) -> c8(MARK(tl(tl(adx(y0))))) A__HD(cons(tl(tl(zeros)), z1)) -> c8(MARK(tl(tl(zeros)))) A__HD(cons(tl(tl(incr(y0))), z1)) -> c8(MARK(tl(tl(incr(y0))))) A__HD(cons(tl(tl(hd(y0))), z1)) -> c8(MARK(tl(tl(hd(y0))))) A__HD(cons(tl(tl(tl(y0))), z1)) -> c8(MARK(tl(tl(tl(y0))))) A__HD(cons(tl(tl(cons(y0, y1))), z1)) -> c8(MARK(tl(tl(cons(y0, y1))))) A__HD(cons(tl(tl(y0)), z1)) -> c8(MARK(tl(tl(y0)))) A__HD(cons(tl(nats), z1)) -> c8(MARK(tl(nats))) MARK(hd(hd(zeros))) -> c16(A__HD(a__hd(a__zeros))) MARK(tl(hd(zeros))) -> c17(A__TL(a__hd(a__zeros))) A__TL(cons(z0, adx(y0))) -> c10(MARK(adx(y0))) A__TL(cons(z0, incr(y0))) -> c10(MARK(incr(y0))) A__TL(cons(z0, hd(cons(y0, y1)))) -> c10(MARK(hd(cons(y0, y1)))) A__TL(cons(z0, tl(cons(y0, y1)))) -> c10(MARK(tl(cons(y0, y1)))) A__TL(cons(z0, hd(adx(nats)))) -> c10(MARK(hd(adx(nats)))) A__TL(cons(z0, hd(adx(adx(y0))))) -> c10(MARK(hd(adx(adx(y0))))) A__TL(cons(z0, hd(adx(zeros)))) -> c10(MARK(hd(adx(zeros)))) A__TL(cons(z0, hd(adx(incr(y0))))) -> c10(MARK(hd(adx(incr(y0))))) A__TL(cons(z0, hd(adx(hd(y0))))) -> c10(MARK(hd(adx(hd(y0))))) A__TL(cons(z0, hd(adx(tl(y0))))) -> c10(MARK(hd(adx(tl(y0))))) A__TL(cons(z0, hd(adx(cons(y0, y1))))) -> c10(MARK(hd(adx(cons(y0, y1))))) A__TL(cons(z0, hd(adx(y0)))) -> c10(MARK(hd(adx(y0)))) A__TL(cons(z0, hd(incr(nats)))) -> c10(MARK(hd(incr(nats)))) A__TL(cons(z0, hd(incr(adx(y0))))) -> c10(MARK(hd(incr(adx(y0))))) A__TL(cons(z0, hd(incr(zeros)))) -> c10(MARK(hd(incr(zeros)))) A__TL(cons(z0, hd(incr(incr(y0))))) -> c10(MARK(hd(incr(incr(y0))))) A__TL(cons(z0, hd(incr(hd(y0))))) -> c10(MARK(hd(incr(hd(y0))))) A__TL(cons(z0, hd(incr(tl(y0))))) -> c10(MARK(hd(incr(tl(y0))))) A__TL(cons(z0, hd(incr(y0)))) -> c10(MARK(hd(incr(y0)))) A__TL(cons(z0, hd(hd(nats)))) -> c10(MARK(hd(hd(nats)))) A__TL(cons(z0, hd(hd(adx(y0))))) -> c10(MARK(hd(hd(adx(y0))))) A__TL(cons(z0, hd(hd(incr(y0))))) -> c10(MARK(hd(hd(incr(y0))))) A__TL(cons(z0, hd(hd(hd(y0))))) -> c10(MARK(hd(hd(hd(y0))))) A__TL(cons(z0, hd(hd(tl(y0))))) -> c10(MARK(hd(hd(tl(y0))))) A__TL(cons(z0, hd(hd(cons(y0, y1))))) -> c10(MARK(hd(hd(cons(y0, y1))))) A__TL(cons(z0, hd(hd(y0)))) -> c10(MARK(hd(hd(y0)))) A__TL(cons(z0, hd(tl(nats)))) -> c10(MARK(hd(tl(nats)))) A__TL(cons(z0, hd(tl(adx(y0))))) -> c10(MARK(hd(tl(adx(y0))))) A__TL(cons(z0, hd(tl(zeros)))) -> c10(MARK(hd(tl(zeros)))) A__TL(cons(z0, hd(tl(incr(y0))))) -> c10(MARK(hd(tl(incr(y0))))) A__TL(cons(z0, hd(tl(hd(y0))))) -> c10(MARK(hd(tl(hd(y0))))) A__TL(cons(z0, hd(tl(tl(y0))))) -> c10(MARK(hd(tl(tl(y0))))) A__TL(cons(z0, hd(tl(cons(y0, y1))))) -> c10(MARK(hd(tl(cons(y0, y1))))) A__TL(cons(z0, hd(tl(y0)))) -> c10(MARK(hd(tl(y0)))) A__TL(cons(z0, hd(nats))) -> c10(MARK(hd(nats))) A__TL(cons(z0, tl(adx(nats)))) -> c10(MARK(tl(adx(nats)))) A__TL(cons(z0, tl(adx(adx(y0))))) -> c10(MARK(tl(adx(adx(y0))))) A__TL(cons(z0, tl(adx(zeros)))) -> c10(MARK(tl(adx(zeros)))) A__TL(cons(z0, tl(adx(incr(y0))))) -> c10(MARK(tl(adx(incr(y0))))) A__TL(cons(z0, tl(adx(hd(y0))))) -> c10(MARK(tl(adx(hd(y0))))) A__TL(cons(z0, tl(adx(tl(y0))))) -> c10(MARK(tl(adx(tl(y0))))) A__TL(cons(z0, tl(adx(cons(y0, y1))))) -> c10(MARK(tl(adx(cons(y0, y1))))) A__TL(cons(z0, tl(adx(s(y0))))) -> c10(MARK(tl(adx(s(y0))))) A__TL(cons(z0, tl(adx(y0)))) -> c10(MARK(tl(adx(y0)))) A__TL(cons(z0, tl(incr(nats)))) -> c10(MARK(tl(incr(nats)))) A__TL(cons(z0, tl(incr(adx(y0))))) -> c10(MARK(tl(incr(adx(y0))))) A__TL(cons(z0, tl(incr(zeros)))) -> c10(MARK(tl(incr(zeros)))) A__TL(cons(z0, tl(incr(incr(y0))))) -> c10(MARK(tl(incr(incr(y0))))) A__TL(cons(z0, tl(incr(hd(y0))))) -> c10(MARK(tl(incr(hd(y0))))) A__TL(cons(z0, tl(incr(tl(y0))))) -> c10(MARK(tl(incr(tl(y0))))) A__TL(cons(z0, tl(incr(cons(y0, y1))))) -> c10(MARK(tl(incr(cons(y0, y1))))) A__TL(cons(z0, tl(incr(0)))) -> c10(MARK(tl(incr(0)))) A__TL(cons(z0, tl(incr(s(y0))))) -> c10(MARK(tl(incr(s(y0))))) A__TL(cons(z0, tl(incr(y0)))) -> c10(MARK(tl(incr(y0)))) A__TL(cons(z0, tl(hd(nats)))) -> c10(MARK(tl(hd(nats)))) A__TL(cons(z0, tl(hd(adx(y0))))) -> c10(MARK(tl(hd(adx(y0))))) A__TL(cons(z0, tl(hd(incr(y0))))) -> c10(MARK(tl(hd(incr(y0))))) A__TL(cons(z0, tl(hd(hd(y0))))) -> c10(MARK(tl(hd(hd(y0))))) A__TL(cons(z0, tl(hd(tl(y0))))) -> c10(MARK(tl(hd(tl(y0))))) A__TL(cons(z0, tl(hd(cons(y0, y1))))) -> c10(MARK(tl(hd(cons(y0, y1))))) A__TL(cons(z0, tl(hd(y0)))) -> c10(MARK(tl(hd(y0)))) A__TL(cons(z0, tl(tl(nats)))) -> c10(MARK(tl(tl(nats)))) A__TL(cons(z0, tl(tl(adx(y0))))) -> c10(MARK(tl(tl(adx(y0))))) A__TL(cons(z0, tl(tl(zeros)))) -> c10(MARK(tl(tl(zeros)))) A__TL(cons(z0, tl(tl(incr(y0))))) -> c10(MARK(tl(tl(incr(y0))))) A__TL(cons(z0, tl(tl(hd(y0))))) -> c10(MARK(tl(tl(hd(y0))))) A__TL(cons(z0, tl(tl(tl(y0))))) -> c10(MARK(tl(tl(tl(y0))))) A__TL(cons(z0, tl(tl(cons(y0, y1))))) -> c10(MARK(tl(tl(cons(y0, y1))))) A__TL(cons(z0, tl(tl(y0)))) -> c10(MARK(tl(tl(y0)))) A__TL(cons(z0, tl(nats))) -> c10(MARK(tl(nats))) A__TL(cons(z0, hd(hd(zeros)))) -> c10(MARK(hd(hd(zeros)))) A__TL(cons(z0, tl(hd(zeros)))) -> c10(MARK(tl(hd(zeros)))) A__TL(cons(z0, tl(adx(0)))) -> c10(MARK(tl(adx(0)))) MARK(hd(tl(zeros))) -> c16(A__HD(a__tl(a__zeros))) MARK(tl(tl(zeros))) -> c17(A__TL(a__tl(a__zeros))) MARK(adx(adx(y0))) -> c13(MARK(adx(y0))) MARK(adx(incr(y0))) -> c13(MARK(incr(y0))) MARK(adx(hd(cons(y0, y1)))) -> c13(MARK(hd(cons(y0, y1)))) MARK(adx(tl(cons(y0, y1)))) -> c13(MARK(tl(cons(y0, y1)))) MARK(adx(hd(adx(nats)))) -> c13(MARK(hd(adx(nats)))) MARK(adx(hd(adx(adx(y0))))) -> c13(MARK(hd(adx(adx(y0))))) MARK(adx(hd(adx(zeros)))) -> c13(MARK(hd(adx(zeros)))) MARK(adx(hd(adx(incr(y0))))) -> c13(MARK(hd(adx(incr(y0))))) MARK(adx(hd(adx(hd(y0))))) -> c13(MARK(hd(adx(hd(y0))))) MARK(adx(hd(adx(tl(y0))))) -> c13(MARK(hd(adx(tl(y0))))) MARK(adx(hd(adx(cons(y0, y1))))) -> c13(MARK(hd(adx(cons(y0, y1))))) MARK(adx(hd(adx(y0)))) -> c13(MARK(hd(adx(y0)))) MARK(adx(hd(incr(nats)))) -> c13(MARK(hd(incr(nats)))) MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) MARK(tl(cons(z0, adx(y1)))) -> c17(A__TL(cons(z0, adx(y1)))) MARK(tl(cons(z0, incr(y1)))) -> c17(A__TL(cons(z0, incr(y1)))) MARK(tl(cons(z0, hd(cons(y1, y2))))) -> c17(A__TL(cons(z0, hd(cons(y1, y2))))) MARK(tl(cons(z0, tl(cons(y1, y2))))) -> c17(A__TL(cons(z0, tl(cons(y1, y2))))) MARK(tl(cons(z0, hd(adx(nats))))) -> c17(A__TL(cons(z0, hd(adx(nats))))) MARK(tl(cons(z0, hd(adx(adx(y1)))))) -> c17(A__TL(cons(z0, hd(adx(adx(y1)))))) MARK(tl(cons(z0, hd(adx(zeros))))) -> c17(A__TL(cons(z0, hd(adx(zeros))))) MARK(tl(cons(z0, hd(adx(incr(y1)))))) -> c17(A__TL(cons(z0, hd(adx(incr(y1)))))) MARK(tl(cons(z0, hd(adx(hd(y1)))))) -> c17(A__TL(cons(z0, hd(adx(hd(y1)))))) MARK(tl(cons(z0, hd(adx(tl(y1)))))) -> c17(A__TL(cons(z0, hd(adx(tl(y1)))))) MARK(tl(cons(z0, hd(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(adx(cons(y1, y2)))))) MARK(tl(cons(z0, hd(adx(y1))))) -> c17(A__TL(cons(z0, hd(adx(y1))))) MARK(tl(cons(z0, hd(incr(nats))))) -> c17(A__TL(cons(z0, hd(incr(nats))))) MARK(tl(cons(z0, hd(incr(adx(y1)))))) -> c17(A__TL(cons(z0, hd(incr(adx(y1)))))) MARK(tl(cons(z0, hd(incr(zeros))))) -> c17(A__TL(cons(z0, hd(incr(zeros))))) MARK(tl(cons(z0, hd(incr(incr(y1)))))) -> c17(A__TL(cons(z0, hd(incr(incr(y1)))))) MARK(tl(cons(z0, hd(incr(hd(y1)))))) -> c17(A__TL(cons(z0, hd(incr(hd(y1)))))) MARK(tl(cons(z0, hd(incr(tl(y1)))))) -> c17(A__TL(cons(z0, hd(incr(tl(y1)))))) MARK(tl(cons(z0, hd(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(incr(cons(y1, y2)))))) MARK(tl(cons(z0, hd(incr(y1))))) -> c17(A__TL(cons(z0, hd(incr(y1))))) MARK(tl(cons(z0, hd(hd(nats))))) -> c17(A__TL(cons(z0, hd(hd(nats))))) MARK(tl(cons(z0, hd(hd(adx(y1)))))) -> c17(A__TL(cons(z0, hd(hd(adx(y1)))))) MARK(tl(cons(z0, hd(hd(incr(y1)))))) -> c17(A__TL(cons(z0, hd(hd(incr(y1)))))) MARK(tl(cons(z0, hd(hd(hd(y1)))))) -> c17(A__TL(cons(z0, hd(hd(hd(y1)))))) MARK(tl(cons(z0, hd(hd(tl(y1)))))) -> c17(A__TL(cons(z0, hd(hd(tl(y1)))))) MARK(tl(cons(z0, hd(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(hd(cons(y1, y2)))))) MARK(tl(cons(z0, hd(hd(y1))))) -> c17(A__TL(cons(z0, hd(hd(y1))))) MARK(tl(cons(z0, hd(tl(nats))))) -> c17(A__TL(cons(z0, hd(tl(nats))))) MARK(tl(cons(z0, hd(tl(adx(y1)))))) -> c17(A__TL(cons(z0, hd(tl(adx(y1)))))) MARK(tl(cons(z0, hd(tl(zeros))))) -> c17(A__TL(cons(z0, hd(tl(zeros))))) MARK(tl(cons(z0, hd(tl(incr(y1)))))) -> c17(A__TL(cons(z0, hd(tl(incr(y1)))))) MARK(tl(cons(z0, hd(tl(hd(y1)))))) -> c17(A__TL(cons(z0, hd(tl(hd(y1)))))) MARK(tl(cons(z0, hd(tl(tl(y1)))))) -> c17(A__TL(cons(z0, hd(tl(tl(y1)))))) MARK(tl(cons(z0, hd(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(tl(cons(y1, y2)))))) MARK(tl(cons(z0, hd(tl(y1))))) -> c17(A__TL(cons(z0, hd(tl(y1))))) MARK(tl(cons(z0, hd(nats)))) -> c17(A__TL(cons(z0, hd(nats)))) MARK(tl(cons(z0, tl(adx(nats))))) -> c17(A__TL(cons(z0, tl(adx(nats))))) MARK(tl(cons(z0, tl(adx(adx(y1)))))) -> c17(A__TL(cons(z0, tl(adx(adx(y1)))))) MARK(tl(cons(z0, tl(adx(zeros))))) -> c17(A__TL(cons(z0, tl(adx(zeros))))) MARK(tl(cons(z0, tl(adx(incr(y1)))))) -> c17(A__TL(cons(z0, tl(adx(incr(y1)))))) MARK(tl(cons(z0, tl(adx(hd(y1)))))) -> c17(A__TL(cons(z0, tl(adx(hd(y1)))))) MARK(tl(cons(z0, tl(adx(tl(y1)))))) -> c17(A__TL(cons(z0, tl(adx(tl(y1)))))) MARK(tl(cons(z0, tl(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(adx(cons(y1, y2)))))) MARK(tl(cons(z0, tl(adx(s(y1)))))) -> c17(A__TL(cons(z0, tl(adx(s(y1)))))) MARK(tl(cons(z0, tl(adx(y1))))) -> c17(A__TL(cons(z0, tl(adx(y1))))) MARK(tl(cons(z0, tl(incr(nats))))) -> c17(A__TL(cons(z0, tl(incr(nats))))) MARK(tl(cons(z0, tl(incr(adx(y1)))))) -> c17(A__TL(cons(z0, tl(incr(adx(y1)))))) MARK(tl(cons(z0, tl(incr(zeros))))) -> c17(A__TL(cons(z0, tl(incr(zeros))))) MARK(tl(cons(z0, tl(incr(incr(y1)))))) -> c17(A__TL(cons(z0, tl(incr(incr(y1)))))) MARK(tl(cons(z0, tl(incr(hd(y1)))))) -> c17(A__TL(cons(z0, tl(incr(hd(y1)))))) MARK(tl(cons(z0, tl(incr(tl(y1)))))) -> c17(A__TL(cons(z0, tl(incr(tl(y1)))))) MARK(tl(cons(z0, tl(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(incr(cons(y1, y2)))))) MARK(tl(cons(z0, tl(incr(0))))) -> c17(A__TL(cons(z0, tl(incr(0))))) MARK(tl(cons(z0, tl(incr(s(y1)))))) -> c17(A__TL(cons(z0, tl(incr(s(y1)))))) MARK(tl(cons(z0, tl(incr(y1))))) -> c17(A__TL(cons(z0, tl(incr(y1))))) MARK(tl(cons(z0, tl(hd(nats))))) -> c17(A__TL(cons(z0, tl(hd(nats))))) MARK(tl(cons(z0, tl(hd(adx(y1)))))) -> c17(A__TL(cons(z0, tl(hd(adx(y1)))))) MARK(tl(cons(z0, tl(hd(incr(y1)))))) -> c17(A__TL(cons(z0, tl(hd(incr(y1)))))) MARK(tl(cons(z0, tl(hd(hd(y1)))))) -> c17(A__TL(cons(z0, tl(hd(hd(y1)))))) MARK(tl(cons(z0, tl(hd(tl(y1)))))) -> c17(A__TL(cons(z0, tl(hd(tl(y1)))))) MARK(tl(cons(z0, tl(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(hd(cons(y1, y2)))))) MARK(tl(cons(z0, tl(hd(y1))))) -> c17(A__TL(cons(z0, tl(hd(y1))))) MARK(tl(cons(z0, tl(tl(nats))))) -> c17(A__TL(cons(z0, tl(tl(nats))))) MARK(tl(cons(z0, tl(tl(adx(y1)))))) -> c17(A__TL(cons(z0, tl(tl(adx(y1)))))) MARK(tl(cons(z0, tl(tl(zeros))))) -> c17(A__TL(cons(z0, tl(tl(zeros))))) MARK(tl(cons(z0, tl(tl(incr(y1)))))) -> c17(A__TL(cons(z0, tl(tl(incr(y1)))))) MARK(tl(cons(z0, tl(tl(hd(y1)))))) -> c17(A__TL(cons(z0, tl(tl(hd(y1)))))) MARK(tl(cons(z0, tl(tl(tl(y1)))))) -> c17(A__TL(cons(z0, tl(tl(tl(y1)))))) MARK(tl(cons(z0, tl(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(tl(cons(y1, y2)))))) MARK(tl(cons(z0, tl(tl(y1))))) -> c17(A__TL(cons(z0, tl(tl(y1))))) MARK(tl(cons(z0, tl(nats)))) -> c17(A__TL(cons(z0, tl(nats)))) MARK(tl(cons(z0, hd(adx(0))))) -> c17(A__TL(cons(z0, hd(adx(0))))) MARK(tl(cons(z0, hd(adx(s(y1)))))) -> c17(A__TL(cons(z0, hd(adx(s(y1)))))) MARK(tl(cons(z0, hd(incr(0))))) -> c17(A__TL(cons(z0, hd(incr(0))))) MARK(tl(cons(z0, hd(incr(s(y1)))))) -> c17(A__TL(cons(z0, hd(incr(s(y1)))))) MARK(tl(cons(z0, hd(hd(zeros))))) -> c17(A__TL(cons(z0, hd(hd(zeros))))) MARK(tl(cons(z0, tl(hd(zeros))))) -> c17(A__TL(cons(z0, tl(hd(zeros))))) MARK(tl(cons(z0, tl(adx(0))))) -> c17(A__TL(cons(z0, tl(adx(0))))) MARK(hd(adx(adx(y0)))) -> c16(MARK(adx(adx(y0)))) MARK(hd(adx(incr(y0)))) -> c16(MARK(adx(incr(y0)))) MARK(hd(adx(hd(cons(y0, y1))))) -> c16(MARK(adx(hd(cons(y0, y1))))) MARK(hd(adx(tl(cons(y0, y1))))) -> c16(MARK(adx(tl(cons(y0, y1))))) MARK(hd(adx(hd(adx(nats))))) -> c16(MARK(adx(hd(adx(nats))))) MARK(hd(adx(hd(adx(adx(y0)))))) -> c16(MARK(adx(hd(adx(adx(y0)))))) MARK(hd(adx(hd(adx(zeros))))) -> c16(MARK(adx(hd(adx(zeros))))) MARK(hd(adx(hd(adx(incr(y0)))))) -> c16(MARK(adx(hd(adx(incr(y0)))))) MARK(hd(adx(hd(adx(hd(y0)))))) -> c16(MARK(adx(hd(adx(hd(y0)))))) MARK(hd(adx(hd(adx(tl(y0)))))) -> c16(MARK(adx(hd(adx(tl(y0)))))) MARK(hd(adx(hd(adx(cons(y0, y1)))))) -> c16(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(hd(adx(hd(adx(y0))))) -> c16(MARK(adx(hd(adx(y0))))) MARK(hd(adx(hd(incr(nats))))) -> c16(MARK(adx(hd(incr(nats))))) MARK(hd(adx(hd(incr(adx(y0)))))) -> c16(MARK(adx(hd(incr(adx(y0)))))) MARK(hd(adx(hd(incr(zeros))))) -> c16(MARK(adx(hd(incr(zeros))))) MARK(hd(adx(hd(incr(incr(y0)))))) -> c16(MARK(adx(hd(incr(incr(y0)))))) MARK(hd(adx(hd(incr(hd(y0)))))) -> c16(MARK(adx(hd(incr(hd(y0)))))) MARK(hd(adx(hd(incr(tl(y0)))))) -> c16(MARK(adx(hd(incr(tl(y0)))))) MARK(hd(adx(hd(incr(cons(y0, y1)))))) -> c16(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(hd(adx(hd(incr(y0))))) -> c16(MARK(adx(hd(incr(y0))))) MARK(hd(adx(hd(hd(nats))))) -> c16(MARK(adx(hd(hd(nats))))) MARK(hd(adx(hd(hd(adx(y0)))))) -> c16(MARK(adx(hd(hd(adx(y0)))))) MARK(hd(adx(hd(hd(incr(y0)))))) -> c16(MARK(adx(hd(hd(incr(y0)))))) MARK(hd(adx(hd(hd(hd(y0)))))) -> c16(MARK(adx(hd(hd(hd(y0)))))) MARK(hd(adx(hd(hd(tl(y0)))))) -> c16(MARK(adx(hd(hd(tl(y0)))))) MARK(hd(adx(hd(hd(cons(y0, y1)))))) -> c16(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(hd(adx(hd(hd(y0))))) -> c16(MARK(adx(hd(hd(y0))))) MARK(hd(adx(hd(tl(nats))))) -> c16(MARK(adx(hd(tl(nats))))) MARK(hd(adx(hd(tl(adx(y0)))))) -> c16(MARK(adx(hd(tl(adx(y0)))))) MARK(hd(adx(hd(tl(incr(y0)))))) -> c16(MARK(adx(hd(tl(incr(y0)))))) MARK(hd(adx(hd(tl(hd(y0)))))) -> c16(MARK(adx(hd(tl(hd(y0)))))) MARK(hd(adx(hd(tl(tl(y0)))))) -> c16(MARK(adx(hd(tl(tl(y0)))))) MARK(hd(adx(hd(tl(cons(y0, y1)))))) -> c16(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(hd(adx(hd(tl(y0))))) -> c16(MARK(adx(hd(tl(y0))))) MARK(hd(adx(hd(nats)))) -> c16(MARK(adx(hd(nats)))) MARK(hd(adx(tl(adx(nats))))) -> c16(MARK(adx(tl(adx(nats))))) MARK(hd(adx(tl(adx(adx(y0)))))) -> c16(MARK(adx(tl(adx(adx(y0)))))) MARK(hd(adx(tl(adx(zeros))))) -> c16(MARK(adx(tl(adx(zeros))))) MARK(hd(adx(tl(adx(incr(y0)))))) -> c16(MARK(adx(tl(adx(incr(y0)))))) MARK(hd(adx(tl(adx(hd(y0)))))) -> c16(MARK(adx(tl(adx(hd(y0)))))) MARK(hd(adx(tl(adx(tl(y0)))))) -> c16(MARK(adx(tl(adx(tl(y0)))))) MARK(hd(adx(tl(adx(cons(y0, y1)))))) -> c16(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(hd(adx(tl(adx(y0))))) -> c16(MARK(adx(tl(adx(y0))))) MARK(hd(adx(tl(incr(nats))))) -> c16(MARK(adx(tl(incr(nats))))) MARK(hd(adx(tl(incr(adx(y0)))))) -> c16(MARK(adx(tl(incr(adx(y0)))))) MARK(hd(adx(tl(incr(zeros))))) -> c16(MARK(adx(tl(incr(zeros))))) MARK(hd(adx(tl(incr(incr(y0)))))) -> c16(MARK(adx(tl(incr(incr(y0)))))) MARK(hd(adx(tl(incr(hd(y0)))))) -> c16(MARK(adx(tl(incr(hd(y0)))))) MARK(hd(adx(tl(incr(tl(y0)))))) -> c16(MARK(adx(tl(incr(tl(y0)))))) MARK(hd(adx(tl(incr(cons(y0, y1)))))) -> c16(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(hd(adx(tl(incr(s(y0)))))) -> c16(MARK(adx(tl(incr(s(y0)))))) MARK(hd(adx(tl(incr(y0))))) -> c16(MARK(adx(tl(incr(y0))))) MARK(hd(adx(tl(hd(nats))))) -> c16(MARK(adx(tl(hd(nats))))) MARK(hd(adx(tl(hd(adx(y0)))))) -> c16(MARK(adx(tl(hd(adx(y0)))))) MARK(hd(adx(tl(hd(incr(y0)))))) -> c16(MARK(adx(tl(hd(incr(y0)))))) MARK(hd(adx(tl(hd(hd(y0)))))) -> c16(MARK(adx(tl(hd(hd(y0)))))) MARK(hd(adx(tl(hd(tl(y0)))))) -> c16(MARK(adx(tl(hd(tl(y0)))))) MARK(hd(adx(tl(hd(cons(y0, y1)))))) -> c16(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(hd(adx(tl(hd(y0))))) -> c16(MARK(adx(tl(hd(y0))))) MARK(hd(adx(tl(tl(nats))))) -> c16(MARK(adx(tl(tl(nats))))) MARK(hd(adx(tl(tl(adx(y0)))))) -> c16(MARK(adx(tl(tl(adx(y0)))))) MARK(hd(adx(tl(tl(incr(y0)))))) -> c16(MARK(adx(tl(tl(incr(y0)))))) MARK(hd(adx(tl(tl(hd(y0)))))) -> c16(MARK(adx(tl(tl(hd(y0)))))) MARK(hd(adx(tl(tl(tl(y0)))))) -> c16(MARK(adx(tl(tl(tl(y0)))))) MARK(hd(adx(tl(tl(cons(y0, y1)))))) -> c16(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(hd(adx(tl(tl(y0))))) -> c16(MARK(adx(tl(tl(y0))))) MARK(hd(adx(tl(nats)))) -> c16(MARK(adx(tl(nats)))) MARK(hd(adx(hd(adx(0))))) -> c16(MARK(adx(hd(adx(0))))) MARK(hd(adx(hd(adx(s(y0)))))) -> c16(MARK(adx(hd(adx(s(y0)))))) MARK(hd(adx(hd(incr(0))))) -> c16(MARK(adx(hd(incr(0))))) MARK(hd(adx(hd(incr(s(y0)))))) -> c16(MARK(adx(hd(incr(s(y0)))))) MARK(hd(adx(hd(hd(zeros))))) -> c16(MARK(adx(hd(hd(zeros))))) MARK(hd(adx(tl(hd(zeros))))) -> c16(MARK(adx(tl(hd(zeros))))) MARK(hd(adx(tl(adx(0))))) -> c16(MARK(adx(tl(adx(0))))) MARK(hd(adx(hd(tl(zeros))))) -> c16(MARK(adx(hd(tl(zeros))))) MARK(hd(adx(tl(tl(zeros))))) -> c16(MARK(adx(tl(tl(zeros))))) MARK(hd(adx(tl(adx(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) MARK(hd(adx(tl(incr(0))))) -> c16(MARK(adx(tl(incr(0))))) MARK(hd(incr(incr(y0)))) -> c16(MARK(incr(incr(y0)))) MARK(hd(incr(hd(cons(y0, y1))))) -> c16(MARK(incr(hd(cons(y0, y1))))) MARK(hd(incr(tl(cons(y0, y1))))) -> c16(MARK(incr(tl(cons(y0, y1))))) MARK(hd(incr(hd(adx(adx(y0)))))) -> c16(MARK(incr(hd(adx(adx(y0)))))) MARK(hd(incr(hd(adx(incr(y0)))))) -> c16(MARK(incr(hd(adx(incr(y0)))))) MARK(hd(incr(hd(adx(hd(y0)))))) -> c16(MARK(incr(hd(adx(hd(y0)))))) MARK(hd(incr(hd(adx(tl(y0)))))) -> c16(MARK(incr(hd(adx(tl(y0)))))) MARK(hd(incr(hd(adx(y0))))) -> c16(MARK(incr(hd(adx(y0))))) MARK(hd(incr(hd(incr(nats))))) -> c16(MARK(incr(hd(incr(nats))))) MARK(hd(incr(hd(incr(adx(y0)))))) -> c16(MARK(incr(hd(incr(adx(y0)))))) MARK(hd(incr(hd(incr(zeros))))) -> c16(MARK(incr(hd(incr(zeros))))) MARK(hd(incr(hd(incr(incr(y0)))))) -> c16(MARK(incr(hd(incr(incr(y0)))))) MARK(hd(incr(hd(incr(hd(y0)))))) -> c16(MARK(incr(hd(incr(hd(y0)))))) MARK(hd(incr(hd(incr(tl(y0)))))) -> c16(MARK(incr(hd(incr(tl(y0)))))) MARK(hd(incr(hd(incr(cons(y0, y1)))))) -> c16(MARK(incr(hd(incr(cons(y0, y1)))))) MARK(hd(incr(hd(incr(y0))))) -> c16(MARK(incr(hd(incr(y0))))) MARK(hd(incr(hd(hd(nats))))) -> c16(MARK(incr(hd(hd(nats))))) MARK(hd(incr(hd(hd(adx(y0)))))) -> c16(MARK(incr(hd(hd(adx(y0)))))) MARK(hd(incr(hd(hd(incr(y0)))))) -> c16(MARK(incr(hd(hd(incr(y0)))))) MARK(hd(incr(hd(hd(hd(y0)))))) -> c16(MARK(incr(hd(hd(hd(y0)))))) MARK(hd(incr(hd(hd(tl(y0)))))) -> c16(MARK(incr(hd(hd(tl(y0)))))) MARK(hd(incr(hd(hd(cons(y0, y1)))))) -> c16(MARK(incr(hd(hd(cons(y0, y1)))))) MARK(hd(incr(hd(hd(y0))))) -> c16(MARK(incr(hd(hd(y0))))) MARK(hd(incr(hd(tl(nats))))) -> c16(MARK(incr(hd(tl(nats))))) MARK(hd(incr(hd(tl(adx(y0)))))) -> c16(MARK(incr(hd(tl(adx(y0)))))) MARK(hd(incr(hd(tl(incr(y0)))))) -> c16(MARK(incr(hd(tl(incr(y0)))))) MARK(hd(incr(hd(tl(hd(y0)))))) -> c16(MARK(incr(hd(tl(hd(y0)))))) MARK(hd(incr(hd(tl(tl(y0)))))) -> c16(MARK(incr(hd(tl(tl(y0)))))) MARK(hd(incr(hd(tl(cons(y0, y1)))))) -> c16(MARK(incr(hd(tl(cons(y0, y1)))))) MARK(hd(incr(hd(tl(y0))))) -> c16(MARK(incr(hd(tl(y0))))) MARK(hd(incr(hd(nats)))) -> c16(MARK(incr(hd(nats)))) MARK(hd(incr(tl(adx(adx(y0)))))) -> c16(MARK(incr(tl(adx(adx(y0)))))) MARK(hd(incr(tl(adx(incr(y0)))))) -> c16(MARK(incr(tl(adx(incr(y0)))))) MARK(hd(incr(tl(adx(hd(y0)))))) -> c16(MARK(incr(tl(adx(hd(y0)))))) MARK(hd(incr(tl(adx(tl(y0)))))) -> c16(MARK(incr(tl(adx(tl(y0)))))) MARK(hd(incr(tl(adx(y0))))) -> c16(MARK(incr(tl(adx(y0))))) MARK(hd(incr(tl(incr(nats))))) -> c16(MARK(incr(tl(incr(nats))))) MARK(hd(incr(tl(incr(adx(y0)))))) -> c16(MARK(incr(tl(incr(adx(y0)))))) MARK(hd(incr(tl(incr(zeros))))) -> c16(MARK(incr(tl(incr(zeros))))) MARK(hd(incr(tl(incr(incr(y0)))))) -> c16(MARK(incr(tl(incr(incr(y0)))))) MARK(hd(incr(tl(incr(hd(y0)))))) -> c16(MARK(incr(tl(incr(hd(y0)))))) MARK(hd(incr(tl(incr(tl(y0)))))) -> c16(MARK(incr(tl(incr(tl(y0)))))) MARK(hd(incr(tl(incr(cons(y0, y1)))))) -> c16(MARK(incr(tl(incr(cons(y0, y1)))))) MARK(hd(incr(tl(incr(y0))))) -> c16(MARK(incr(tl(incr(y0))))) MARK(hd(incr(tl(hd(nats))))) -> c16(MARK(incr(tl(hd(nats))))) MARK(hd(incr(tl(hd(adx(y0)))))) -> c16(MARK(incr(tl(hd(adx(y0)))))) MARK(hd(incr(tl(hd(incr(y0)))))) -> c16(MARK(incr(tl(hd(incr(y0)))))) MARK(hd(incr(tl(hd(hd(y0)))))) -> c16(MARK(incr(tl(hd(hd(y0)))))) MARK(hd(incr(tl(hd(tl(y0)))))) -> c16(MARK(incr(tl(hd(tl(y0)))))) MARK(hd(incr(tl(hd(cons(y0, y1)))))) -> c16(MARK(incr(tl(hd(cons(y0, y1)))))) MARK(hd(incr(tl(hd(y0))))) -> c16(MARK(incr(tl(hd(y0))))) MARK(hd(incr(tl(tl(nats))))) -> c16(MARK(incr(tl(tl(nats))))) MARK(hd(incr(tl(tl(adx(y0)))))) -> c16(MARK(incr(tl(tl(adx(y0)))))) MARK(hd(incr(tl(tl(incr(y0)))))) -> c16(MARK(incr(tl(tl(incr(y0)))))) MARK(hd(incr(tl(tl(hd(y0)))))) -> c16(MARK(incr(tl(tl(hd(y0)))))) MARK(hd(incr(tl(tl(tl(y0)))))) -> c16(MARK(incr(tl(tl(tl(y0)))))) MARK(hd(incr(tl(tl(cons(y0, y1)))))) -> c16(MARK(incr(tl(tl(cons(y0, y1)))))) MARK(hd(incr(tl(tl(y0))))) -> c16(MARK(incr(tl(tl(y0))))) MARK(hd(incr(tl(nats)))) -> c16(MARK(incr(tl(nats)))) MARK(hd(incr(hd(incr(0))))) -> c16(MARK(incr(hd(incr(0))))) MARK(hd(incr(hd(incr(s(y0)))))) -> c16(MARK(incr(hd(incr(s(y0)))))) MARK(hd(incr(hd(hd(zeros))))) -> c16(MARK(incr(hd(hd(zeros))))) MARK(hd(incr(tl(hd(zeros))))) -> c16(MARK(incr(tl(hd(zeros))))) MARK(hd(incr(hd(tl(zeros))))) -> c16(MARK(incr(hd(tl(zeros))))) MARK(hd(incr(tl(tl(zeros))))) -> c16(MARK(incr(tl(tl(zeros))))) MARK(hd(incr(tl(incr(0))))) -> c16(MARK(incr(tl(incr(0))))) MARK(hd(incr(adx(adx(y0))))) -> c16(MARK(incr(adx(adx(y0))))) MARK(hd(incr(adx(incr(y0))))) -> c16(MARK(incr(adx(incr(y0))))) MARK(hd(incr(adx(hd(cons(y0, y1)))))) -> c16(MARK(incr(adx(hd(cons(y0, y1)))))) MARK(hd(incr(adx(tl(cons(y0, y1)))))) -> c16(MARK(incr(adx(tl(cons(y0, y1)))))) MARK(hd(incr(adx(hd(adx(nats)))))) -> c16(MARK(incr(adx(hd(adx(nats)))))) MARK(hd(incr(adx(hd(adx(adx(y0))))))) -> c16(MARK(incr(adx(hd(adx(adx(y0))))))) MARK(hd(incr(adx(hd(adx(zeros)))))) -> c16(MARK(incr(adx(hd(adx(zeros)))))) MARK(hd(incr(adx(hd(adx(incr(y0))))))) -> c16(MARK(incr(adx(hd(adx(incr(y0))))))) MARK(hd(incr(adx(hd(adx(hd(y0))))))) -> c16(MARK(incr(adx(hd(adx(hd(y0))))))) MARK(hd(incr(adx(hd(adx(tl(y0))))))) -> c16(MARK(incr(adx(hd(adx(tl(y0))))))) MARK(hd(incr(adx(hd(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(adx(cons(y0, y1))))))) MARK(hd(incr(adx(hd(adx(y0)))))) -> c16(MARK(incr(adx(hd(adx(y0)))))) MARK(hd(incr(adx(hd(incr(nats)))))) -> c16(MARK(incr(adx(hd(incr(nats)))))) MARK(hd(incr(adx(hd(incr(adx(y0))))))) -> c16(MARK(incr(adx(hd(incr(adx(y0))))))) MARK(hd(incr(adx(hd(incr(zeros)))))) -> c16(MARK(incr(adx(hd(incr(zeros)))))) MARK(hd(incr(adx(hd(incr(incr(y0))))))) -> c16(MARK(incr(adx(hd(incr(incr(y0))))))) MARK(hd(incr(adx(hd(incr(hd(y0))))))) -> c16(MARK(incr(adx(hd(incr(hd(y0))))))) MARK(hd(incr(adx(hd(incr(tl(y0))))))) -> c16(MARK(incr(adx(hd(incr(tl(y0))))))) MARK(hd(incr(adx(hd(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(incr(cons(y0, y1))))))) MARK(hd(incr(adx(hd(incr(y0)))))) -> c16(MARK(incr(adx(hd(incr(y0)))))) MARK(hd(incr(adx(hd(hd(nats)))))) -> c16(MARK(incr(adx(hd(hd(nats)))))) MARK(hd(incr(adx(hd(hd(adx(y0))))))) -> c16(MARK(incr(adx(hd(hd(adx(y0))))))) MARK(hd(incr(adx(hd(hd(incr(y0))))))) -> c16(MARK(incr(adx(hd(hd(incr(y0))))))) MARK(hd(incr(adx(hd(hd(hd(y0))))))) -> c16(MARK(incr(adx(hd(hd(hd(y0))))))) MARK(hd(incr(adx(hd(hd(tl(y0))))))) -> c16(MARK(incr(adx(hd(hd(tl(y0))))))) MARK(hd(incr(adx(hd(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(hd(cons(y0, y1))))))) MARK(hd(incr(adx(hd(hd(y0)))))) -> c16(MARK(incr(adx(hd(hd(y0)))))) MARK(hd(incr(adx(hd(tl(nats)))))) -> c16(MARK(incr(adx(hd(tl(nats)))))) MARK(hd(incr(adx(hd(tl(adx(y0))))))) -> c16(MARK(incr(adx(hd(tl(adx(y0))))))) MARK(hd(incr(adx(hd(tl(incr(y0))))))) -> c16(MARK(incr(adx(hd(tl(incr(y0))))))) MARK(hd(incr(adx(hd(tl(hd(y0))))))) -> c16(MARK(incr(adx(hd(tl(hd(y0))))))) MARK(hd(incr(adx(hd(tl(tl(y0))))))) -> c16(MARK(incr(adx(hd(tl(tl(y0))))))) MARK(hd(incr(adx(hd(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(tl(cons(y0, y1))))))) MARK(hd(incr(adx(hd(tl(y0)))))) -> c16(MARK(incr(adx(hd(tl(y0)))))) MARK(hd(incr(adx(hd(nats))))) -> c16(MARK(incr(adx(hd(nats))))) MARK(hd(incr(adx(tl(adx(nats)))))) -> c16(MARK(incr(adx(tl(adx(nats)))))) MARK(hd(incr(adx(tl(adx(adx(y0))))))) -> c16(MARK(incr(adx(tl(adx(adx(y0))))))) MARK(hd(incr(adx(tl(adx(zeros)))))) -> c16(MARK(incr(adx(tl(adx(zeros)))))) MARK(hd(incr(adx(tl(adx(incr(y0))))))) -> c16(MARK(incr(adx(tl(adx(incr(y0))))))) MARK(hd(incr(adx(tl(adx(hd(y0))))))) -> c16(MARK(incr(adx(tl(adx(hd(y0))))))) MARK(hd(incr(adx(tl(adx(tl(y0))))))) -> c16(MARK(incr(adx(tl(adx(tl(y0))))))) MARK(hd(incr(adx(tl(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(adx(cons(y0, y1))))))) MARK(hd(incr(adx(tl(adx(y0)))))) -> c16(MARK(incr(adx(tl(adx(y0)))))) MARK(hd(incr(adx(tl(incr(nats)))))) -> c16(MARK(incr(adx(tl(incr(nats)))))) MARK(hd(incr(adx(tl(incr(adx(y0))))))) -> c16(MARK(incr(adx(tl(incr(adx(y0))))))) MARK(hd(incr(adx(tl(incr(zeros)))))) -> c16(MARK(incr(adx(tl(incr(zeros)))))) MARK(hd(incr(adx(tl(incr(incr(y0))))))) -> c16(MARK(incr(adx(tl(incr(incr(y0))))))) MARK(hd(incr(adx(tl(incr(hd(y0))))))) -> c16(MARK(incr(adx(tl(incr(hd(y0))))))) MARK(hd(incr(adx(tl(incr(tl(y0))))))) -> c16(MARK(incr(adx(tl(incr(tl(y0))))))) MARK(hd(incr(adx(tl(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(incr(cons(y0, y1))))))) MARK(hd(incr(adx(tl(incr(s(y0))))))) -> c16(MARK(incr(adx(tl(incr(s(y0))))))) MARK(hd(incr(adx(tl(incr(y0)))))) -> c16(MARK(incr(adx(tl(incr(y0)))))) MARK(hd(incr(adx(tl(hd(nats)))))) -> c16(MARK(incr(adx(tl(hd(nats)))))) MARK(hd(incr(adx(tl(hd(adx(y0))))))) -> c16(MARK(incr(adx(tl(hd(adx(y0))))))) MARK(hd(incr(adx(tl(hd(incr(y0))))))) -> c16(MARK(incr(adx(tl(hd(incr(y0))))))) MARK(hd(incr(adx(tl(hd(hd(y0))))))) -> c16(MARK(incr(adx(tl(hd(hd(y0))))))) MARK(hd(incr(adx(tl(hd(tl(y0))))))) -> c16(MARK(incr(adx(tl(hd(tl(y0))))))) MARK(hd(incr(adx(tl(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(hd(cons(y0, y1))))))) MARK(hd(incr(adx(tl(hd(y0)))))) -> c16(MARK(incr(adx(tl(hd(y0)))))) MARK(hd(incr(adx(tl(tl(nats)))))) -> c16(MARK(incr(adx(tl(tl(nats)))))) MARK(hd(incr(adx(tl(tl(adx(y0))))))) -> c16(MARK(incr(adx(tl(tl(adx(y0))))))) MARK(hd(incr(adx(tl(tl(incr(y0))))))) -> c16(MARK(incr(adx(tl(tl(incr(y0))))))) MARK(hd(incr(adx(tl(tl(hd(y0))))))) -> c16(MARK(incr(adx(tl(tl(hd(y0))))))) MARK(hd(incr(adx(tl(tl(tl(y0))))))) -> c16(MARK(incr(adx(tl(tl(tl(y0))))))) MARK(hd(incr(adx(tl(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(tl(cons(y0, y1))))))) MARK(hd(incr(adx(tl(tl(y0)))))) -> c16(MARK(incr(adx(tl(tl(y0)))))) MARK(hd(incr(adx(tl(nats))))) -> c16(MARK(incr(adx(tl(nats))))) MARK(hd(incr(adx(hd(adx(0)))))) -> c16(MARK(incr(adx(hd(adx(0)))))) MARK(hd(incr(adx(hd(adx(s(y0))))))) -> c16(MARK(incr(adx(hd(adx(s(y0))))))) MARK(hd(incr(adx(hd(incr(0)))))) -> c16(MARK(incr(adx(hd(incr(0)))))) MARK(hd(incr(adx(hd(incr(s(y0))))))) -> c16(MARK(incr(adx(hd(incr(s(y0))))))) MARK(hd(incr(adx(hd(hd(zeros)))))) -> c16(MARK(incr(adx(hd(hd(zeros)))))) MARK(hd(incr(adx(tl(hd(zeros)))))) -> c16(MARK(incr(adx(tl(hd(zeros)))))) MARK(hd(incr(adx(tl(adx(0)))))) -> c16(MARK(incr(adx(tl(adx(0)))))) MARK(hd(incr(adx(hd(tl(zeros)))))) -> c16(MARK(incr(adx(hd(tl(zeros)))))) MARK(hd(incr(adx(tl(tl(zeros)))))) -> c16(MARK(incr(adx(tl(tl(zeros)))))) MARK(hd(incr(adx(tl(adx(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) MARK(hd(incr(adx(tl(incr(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) MARK(hd(incr(hd(adx(nats))))) -> c16(MARK(incr(hd(adx(nats))))) MARK(hd(incr(hd(adx(zeros))))) -> c16(MARK(incr(hd(adx(zeros))))) MARK(hd(incr(hd(adx(cons(y0, y1)))))) -> c16(MARK(incr(hd(adx(cons(y0, y1)))))) MARK(hd(incr(tl(adx(nats))))) -> c16(MARK(incr(tl(adx(nats))))) MARK(hd(incr(tl(adx(zeros))))) -> c16(MARK(incr(tl(adx(zeros))))) MARK(hd(incr(tl(adx(cons(y0, y1)))))) -> c16(MARK(incr(tl(adx(cons(y0, y1)))))) MARK(hd(incr(tl(incr(s(y0)))))) -> c16(MARK(incr(tl(incr(s(y0)))))) MARK(hd(hd(adx(adx(y0))))) -> c16(MARK(hd(adx(adx(y0))))) MARK(hd(hd(adx(incr(y0))))) -> c16(MARK(hd(adx(incr(y0))))) MARK(hd(hd(adx(hd(y0))))) -> c16(MARK(hd(adx(hd(y0))))) MARK(hd(hd(adx(tl(y0))))) -> c16(MARK(hd(adx(tl(y0))))) MARK(hd(hd(incr(adx(y0))))) -> c16(MARK(hd(incr(adx(y0))))) MARK(hd(hd(incr(incr(y0))))) -> c16(MARK(hd(incr(incr(y0))))) MARK(hd(hd(incr(hd(y0))))) -> c16(MARK(hd(incr(hd(y0))))) MARK(hd(hd(incr(tl(y0))))) -> c16(MARK(hd(incr(tl(y0))))) MARK(hd(hd(hd(nats)))) -> c16(MARK(hd(hd(nats)))) MARK(hd(hd(hd(adx(y0))))) -> c16(MARK(hd(hd(adx(y0))))) MARK(hd(hd(hd(incr(y0))))) -> c16(MARK(hd(hd(incr(y0))))) MARK(hd(hd(hd(hd(y0))))) -> c16(MARK(hd(hd(hd(y0))))) MARK(hd(hd(hd(tl(y0))))) -> c16(MARK(hd(hd(tl(y0))))) MARK(hd(hd(hd(cons(y0, y1))))) -> c16(MARK(hd(hd(cons(y0, y1))))) MARK(hd(hd(hd(y0)))) -> c16(MARK(hd(hd(y0)))) MARK(hd(hd(tl(nats)))) -> c16(MARK(hd(tl(nats)))) MARK(hd(hd(tl(adx(y0))))) -> c16(MARK(hd(tl(adx(y0))))) MARK(hd(hd(tl(incr(y0))))) -> c16(MARK(hd(tl(incr(y0))))) MARK(hd(hd(tl(hd(y0))))) -> c16(MARK(hd(tl(hd(y0))))) MARK(hd(hd(tl(tl(y0))))) -> c16(MARK(hd(tl(tl(y0))))) MARK(hd(hd(tl(cons(y0, y1))))) -> c16(MARK(hd(tl(cons(y0, y1))))) MARK(hd(hd(tl(y0)))) -> c16(MARK(hd(tl(y0)))) MARK(hd(hd(nats))) -> c16(MARK(hd(nats))) MARK(hd(hd(hd(zeros)))) -> c16(MARK(hd(hd(zeros)))) MARK(hd(hd(tl(zeros)))) -> c16(MARK(hd(tl(zeros)))) MARK(hd(hd(adx(nats)))) -> c16(MARK(hd(adx(nats)))) MARK(hd(hd(adx(zeros)))) -> c16(MARK(hd(adx(zeros)))) MARK(hd(hd(adx(cons(y0, y1))))) -> c16(MARK(hd(adx(cons(y0, y1))))) MARK(hd(hd(incr(nats)))) -> c16(MARK(hd(incr(nats)))) MARK(hd(hd(incr(zeros)))) -> c16(MARK(hd(incr(zeros)))) MARK(hd(hd(cons(adx(y0), y1)))) -> c16(MARK(hd(cons(adx(y0), y1)))) MARK(hd(hd(cons(incr(y0), y1)))) -> c16(MARK(hd(cons(incr(y0), y1)))) MARK(hd(hd(cons(hd(cons(y0, y1)), y2)))) -> c16(MARK(hd(cons(hd(cons(y0, y1)), y2)))) MARK(hd(hd(cons(tl(cons(y0, y1)), y2)))) -> c16(MARK(hd(cons(tl(cons(y0, y1)), y2)))) MARK(hd(hd(cons(hd(adx(nats)), y0)))) -> c16(MARK(hd(cons(hd(adx(nats)), y0)))) MARK(hd(hd(cons(hd(adx(adx(y0))), y1)))) -> c16(MARK(hd(cons(hd(adx(adx(y0))), y1)))) MARK(hd(hd(cons(hd(adx(zeros)), y0)))) -> c16(MARK(hd(cons(hd(adx(zeros)), y0)))) MARK(hd(hd(cons(hd(adx(incr(y0))), y1)))) -> c16(MARK(hd(cons(hd(adx(incr(y0))), y1)))) MARK(hd(hd(cons(hd(adx(hd(y0))), y1)))) -> c16(MARK(hd(cons(hd(adx(hd(y0))), y1)))) MARK(hd(hd(cons(hd(adx(tl(y0))), y1)))) -> c16(MARK(hd(cons(hd(adx(tl(y0))), y1)))) MARK(hd(hd(cons(hd(adx(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(hd(adx(cons(y0, y1))), y2)))) MARK(hd(hd(cons(hd(adx(y0)), y1)))) -> c16(MARK(hd(cons(hd(adx(y0)), y1)))) MARK(hd(hd(cons(hd(incr(nats)), y0)))) -> c16(MARK(hd(cons(hd(incr(nats)), y0)))) MARK(hd(hd(cons(hd(incr(adx(y0))), y1)))) -> c16(MARK(hd(cons(hd(incr(adx(y0))), y1)))) MARK(hd(hd(cons(hd(incr(zeros)), y0)))) -> c16(MARK(hd(cons(hd(incr(zeros)), y0)))) MARK(hd(hd(cons(hd(incr(incr(y0))), y1)))) -> c16(MARK(hd(cons(hd(incr(incr(y0))), y1)))) MARK(hd(hd(cons(hd(incr(hd(y0))), y1)))) -> c16(MARK(hd(cons(hd(incr(hd(y0))), y1)))) MARK(hd(hd(cons(hd(incr(tl(y0))), y1)))) -> c16(MARK(hd(cons(hd(incr(tl(y0))), y1)))) MARK(hd(hd(cons(hd(incr(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(hd(incr(cons(y0, y1))), y2)))) MARK(hd(hd(cons(hd(incr(y0)), y1)))) -> c16(MARK(hd(cons(hd(incr(y0)), y1)))) MARK(hd(hd(cons(hd(hd(nats)), y0)))) -> c16(MARK(hd(cons(hd(hd(nats)), y0)))) MARK(hd(hd(cons(hd(hd(adx(y0))), y1)))) -> c16(MARK(hd(cons(hd(hd(adx(y0))), y1)))) MARK(hd(hd(cons(hd(hd(zeros)), y0)))) -> c16(MARK(hd(cons(hd(hd(zeros)), y0)))) MARK(hd(hd(cons(hd(hd(incr(y0))), y1)))) -> c16(MARK(hd(cons(hd(hd(incr(y0))), y1)))) MARK(hd(hd(cons(hd(hd(hd(y0))), y1)))) -> c16(MARK(hd(cons(hd(hd(hd(y0))), y1)))) MARK(hd(hd(cons(hd(hd(tl(y0))), y1)))) -> c16(MARK(hd(cons(hd(hd(tl(y0))), y1)))) MARK(hd(hd(cons(hd(hd(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(hd(hd(cons(y0, y1))), y2)))) MARK(hd(hd(cons(hd(hd(y0)), y1)))) -> c16(MARK(hd(cons(hd(hd(y0)), y1)))) MARK(hd(hd(cons(hd(tl(nats)), y0)))) -> c16(MARK(hd(cons(hd(tl(nats)), y0)))) MARK(hd(hd(cons(hd(tl(adx(y0))), y1)))) -> c16(MARK(hd(cons(hd(tl(adx(y0))), y1)))) MARK(hd(hd(cons(hd(tl(zeros)), y0)))) -> c16(MARK(hd(cons(hd(tl(zeros)), y0)))) MARK(hd(hd(cons(hd(tl(incr(y0))), y1)))) -> c16(MARK(hd(cons(hd(tl(incr(y0))), y1)))) MARK(hd(hd(cons(hd(tl(hd(y0))), y1)))) -> c16(MARK(hd(cons(hd(tl(hd(y0))), y1)))) MARK(hd(hd(cons(hd(tl(tl(y0))), y1)))) -> c16(MARK(hd(cons(hd(tl(tl(y0))), y1)))) MARK(hd(hd(cons(hd(tl(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(hd(tl(cons(y0, y1))), y2)))) MARK(hd(hd(cons(hd(tl(y0)), y1)))) -> c16(MARK(hd(cons(hd(tl(y0)), y1)))) MARK(hd(hd(cons(hd(nats), y0)))) -> c16(MARK(hd(cons(hd(nats), y0)))) MARK(hd(hd(cons(tl(adx(nats)), y0)))) -> c16(MARK(hd(cons(tl(adx(nats)), y0)))) MARK(hd(hd(cons(tl(adx(adx(y0))), y1)))) -> c16(MARK(hd(cons(tl(adx(adx(y0))), y1)))) MARK(hd(hd(cons(tl(adx(zeros)), y0)))) -> c16(MARK(hd(cons(tl(adx(zeros)), y0)))) MARK(hd(hd(cons(tl(adx(incr(y0))), y1)))) -> c16(MARK(hd(cons(tl(adx(incr(y0))), y1)))) MARK(hd(hd(cons(tl(adx(hd(y0))), y1)))) -> c16(MARK(hd(cons(tl(adx(hd(y0))), y1)))) MARK(hd(hd(cons(tl(adx(tl(y0))), y1)))) -> c16(MARK(hd(cons(tl(adx(tl(y0))), y1)))) MARK(hd(hd(cons(tl(adx(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(tl(adx(cons(y0, y1))), y2)))) MARK(hd(hd(cons(tl(adx(0)), y0)))) -> c16(MARK(hd(cons(tl(adx(0)), y0)))) MARK(hd(hd(cons(tl(adx(s(y0))), y1)))) -> c16(MARK(hd(cons(tl(adx(s(y0))), y1)))) MARK(hd(hd(cons(tl(adx(y0)), y1)))) -> c16(MARK(hd(cons(tl(adx(y0)), y1)))) MARK(hd(hd(cons(tl(incr(nats)), y0)))) -> c16(MARK(hd(cons(tl(incr(nats)), y0)))) MARK(hd(hd(cons(tl(incr(adx(y0))), y1)))) -> c16(MARK(hd(cons(tl(incr(adx(y0))), y1)))) MARK(hd(hd(cons(tl(incr(zeros)), y0)))) -> c16(MARK(hd(cons(tl(incr(zeros)), y0)))) MARK(hd(hd(cons(tl(incr(incr(y0))), y1)))) -> c16(MARK(hd(cons(tl(incr(incr(y0))), y1)))) MARK(hd(hd(cons(tl(incr(hd(y0))), y1)))) -> c16(MARK(hd(cons(tl(incr(hd(y0))), y1)))) MARK(hd(hd(cons(tl(incr(tl(y0))), y1)))) -> c16(MARK(hd(cons(tl(incr(tl(y0))), y1)))) MARK(hd(hd(cons(tl(incr(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(tl(incr(cons(y0, y1))), y2)))) MARK(hd(hd(cons(tl(incr(0)), y0)))) -> c16(MARK(hd(cons(tl(incr(0)), y0)))) MARK(hd(hd(cons(tl(incr(s(y0))), y1)))) -> c16(MARK(hd(cons(tl(incr(s(y0))), y1)))) MARK(hd(hd(cons(tl(incr(y0)), y1)))) -> c16(MARK(hd(cons(tl(incr(y0)), y1)))) MARK(hd(hd(cons(tl(hd(nats)), y0)))) -> c16(MARK(hd(cons(tl(hd(nats)), y0)))) MARK(hd(hd(cons(tl(hd(adx(y0))), y1)))) -> c16(MARK(hd(cons(tl(hd(adx(y0))), y1)))) MARK(hd(hd(cons(tl(hd(zeros)), y0)))) -> c16(MARK(hd(cons(tl(hd(zeros)), y0)))) MARK(hd(hd(cons(tl(hd(incr(y0))), y1)))) -> c16(MARK(hd(cons(tl(hd(incr(y0))), y1)))) MARK(hd(hd(cons(tl(hd(hd(y0))), y1)))) -> c16(MARK(hd(cons(tl(hd(hd(y0))), y1)))) MARK(hd(hd(cons(tl(hd(tl(y0))), y1)))) -> c16(MARK(hd(cons(tl(hd(tl(y0))), y1)))) MARK(hd(hd(cons(tl(hd(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(tl(hd(cons(y0, y1))), y2)))) MARK(hd(hd(cons(tl(hd(y0)), y1)))) -> c16(MARK(hd(cons(tl(hd(y0)), y1)))) MARK(hd(hd(cons(tl(tl(nats)), y0)))) -> c16(MARK(hd(cons(tl(tl(nats)), y0)))) MARK(hd(hd(cons(tl(tl(adx(y0))), y1)))) -> c16(MARK(hd(cons(tl(tl(adx(y0))), y1)))) MARK(hd(hd(cons(tl(tl(zeros)), y0)))) -> c16(MARK(hd(cons(tl(tl(zeros)), y0)))) MARK(hd(hd(cons(tl(tl(incr(y0))), y1)))) -> c16(MARK(hd(cons(tl(tl(incr(y0))), y1)))) MARK(hd(hd(cons(tl(tl(hd(y0))), y1)))) -> c16(MARK(hd(cons(tl(tl(hd(y0))), y1)))) MARK(hd(hd(cons(tl(tl(tl(y0))), y1)))) -> c16(MARK(hd(cons(tl(tl(tl(y0))), y1)))) MARK(hd(hd(cons(tl(tl(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(tl(tl(cons(y0, y1))), y2)))) MARK(hd(hd(cons(tl(tl(y0)), y1)))) -> c16(MARK(hd(cons(tl(tl(y0)), y1)))) MARK(hd(hd(cons(tl(nats), y0)))) -> c16(MARK(hd(cons(tl(nats), y0)))) MARK(hd(hd(cons(hd(adx(0)), y0)))) -> c16(MARK(hd(cons(hd(adx(0)), y0)))) MARK(hd(hd(cons(hd(adx(s(y0))), y1)))) -> c16(MARK(hd(cons(hd(adx(s(y0))), y1)))) MARK(hd(hd(cons(hd(incr(0)), y0)))) -> c16(MARK(hd(cons(hd(incr(0)), y0)))) MARK(hd(hd(cons(hd(incr(s(y0))), y1)))) -> c16(MARK(hd(cons(hd(incr(s(y0))), y1)))) MARK(hd(hd(adx(hd(cons(y0, y1)))))) -> c16(MARK(hd(adx(hd(cons(y0, y1)))))) MARK(hd(hd(adx(tl(cons(y0, y1)))))) -> c16(MARK(hd(adx(tl(cons(y0, y1)))))) MARK(hd(hd(adx(hd(adx(nats)))))) -> c16(MARK(hd(adx(hd(adx(nats)))))) MARK(hd(hd(adx(hd(adx(adx(y0))))))) -> c16(MARK(hd(adx(hd(adx(adx(y0))))))) MARK(hd(hd(adx(hd(adx(zeros)))))) -> c16(MARK(hd(adx(hd(adx(zeros)))))) MARK(hd(hd(adx(hd(adx(incr(y0))))))) -> c16(MARK(hd(adx(hd(adx(incr(y0))))))) MARK(hd(hd(adx(hd(adx(hd(y0))))))) -> c16(MARK(hd(adx(hd(adx(hd(y0))))))) MARK(hd(hd(adx(hd(adx(tl(y0))))))) -> c16(MARK(hd(adx(hd(adx(tl(y0))))))) MARK(hd(hd(adx(hd(adx(cons(y0, y1))))))) -> c16(MARK(hd(adx(hd(adx(cons(y0, y1))))))) MARK(hd(hd(adx(hd(adx(y0)))))) -> c16(MARK(hd(adx(hd(adx(y0)))))) MARK(hd(hd(adx(hd(incr(nats)))))) -> c16(MARK(hd(adx(hd(incr(nats)))))) MARK(hd(hd(adx(hd(incr(adx(y0))))))) -> c16(MARK(hd(adx(hd(incr(adx(y0))))))) MARK(hd(hd(adx(hd(incr(zeros)))))) -> c16(MARK(hd(adx(hd(incr(zeros)))))) MARK(hd(hd(adx(hd(incr(incr(y0))))))) -> c16(MARK(hd(adx(hd(incr(incr(y0))))))) MARK(hd(hd(adx(hd(incr(hd(y0))))))) -> c16(MARK(hd(adx(hd(incr(hd(y0))))))) MARK(hd(hd(adx(hd(incr(tl(y0))))))) -> c16(MARK(hd(adx(hd(incr(tl(y0))))))) MARK(hd(hd(adx(hd(incr(cons(y0, y1))))))) -> c16(MARK(hd(adx(hd(incr(cons(y0, y1))))))) MARK(hd(hd(adx(hd(incr(y0)))))) -> c16(MARK(hd(adx(hd(incr(y0)))))) MARK(hd(hd(adx(hd(hd(nats)))))) -> c16(MARK(hd(adx(hd(hd(nats)))))) MARK(hd(hd(adx(hd(hd(adx(y0))))))) -> c16(MARK(hd(adx(hd(hd(adx(y0))))))) MARK(hd(hd(adx(hd(hd(incr(y0))))))) -> c16(MARK(hd(adx(hd(hd(incr(y0))))))) MARK(hd(hd(adx(hd(hd(hd(y0))))))) -> c16(MARK(hd(adx(hd(hd(hd(y0))))))) MARK(hd(hd(adx(hd(hd(tl(y0))))))) -> c16(MARK(hd(adx(hd(hd(tl(y0))))))) MARK(hd(hd(adx(hd(hd(cons(y0, y1))))))) -> c16(MARK(hd(adx(hd(hd(cons(y0, y1))))))) MARK(hd(hd(adx(hd(hd(y0)))))) -> c16(MARK(hd(adx(hd(hd(y0)))))) MARK(hd(hd(adx(hd(tl(nats)))))) -> c16(MARK(hd(adx(hd(tl(nats)))))) MARK(hd(hd(adx(hd(tl(adx(y0))))))) -> c16(MARK(hd(adx(hd(tl(adx(y0))))))) MARK(hd(hd(adx(hd(tl(incr(y0))))))) -> c16(MARK(hd(adx(hd(tl(incr(y0))))))) MARK(hd(hd(adx(hd(tl(hd(y0))))))) -> c16(MARK(hd(adx(hd(tl(hd(y0))))))) MARK(hd(hd(adx(hd(tl(tl(y0))))))) -> c16(MARK(hd(adx(hd(tl(tl(y0))))))) MARK(hd(hd(adx(hd(tl(cons(y0, y1))))))) -> c16(MARK(hd(adx(hd(tl(cons(y0, y1))))))) MARK(hd(hd(adx(hd(tl(y0)))))) -> c16(MARK(hd(adx(hd(tl(y0)))))) MARK(hd(hd(adx(hd(nats))))) -> c16(MARK(hd(adx(hd(nats))))) MARK(hd(hd(adx(tl(adx(nats)))))) -> c16(MARK(hd(adx(tl(adx(nats)))))) MARK(hd(hd(adx(tl(adx(adx(y0))))))) -> c16(MARK(hd(adx(tl(adx(adx(y0))))))) MARK(hd(hd(adx(tl(adx(zeros)))))) -> c16(MARK(hd(adx(tl(adx(zeros)))))) MARK(hd(hd(adx(tl(adx(incr(y0))))))) -> c16(MARK(hd(adx(tl(adx(incr(y0))))))) MARK(hd(hd(adx(tl(adx(hd(y0))))))) -> c16(MARK(hd(adx(tl(adx(hd(y0))))))) MARK(hd(hd(adx(tl(adx(tl(y0))))))) -> c16(MARK(hd(adx(tl(adx(tl(y0))))))) MARK(hd(hd(adx(tl(adx(cons(y0, y1))))))) -> c16(MARK(hd(adx(tl(adx(cons(y0, y1))))))) MARK(hd(hd(adx(tl(adx(y0)))))) -> c16(MARK(hd(adx(tl(adx(y0)))))) MARK(hd(hd(adx(tl(incr(nats)))))) -> c16(MARK(hd(adx(tl(incr(nats)))))) MARK(hd(hd(adx(tl(incr(adx(y0))))))) -> c16(MARK(hd(adx(tl(incr(adx(y0))))))) MARK(hd(hd(adx(tl(incr(zeros)))))) -> c16(MARK(hd(adx(tl(incr(zeros)))))) MARK(hd(hd(adx(tl(incr(incr(y0))))))) -> c16(MARK(hd(adx(tl(incr(incr(y0))))))) MARK(hd(hd(adx(tl(incr(hd(y0))))))) -> c16(MARK(hd(adx(tl(incr(hd(y0))))))) MARK(hd(hd(adx(tl(incr(tl(y0))))))) -> c16(MARK(hd(adx(tl(incr(tl(y0))))))) MARK(hd(hd(adx(tl(incr(cons(y0, y1))))))) -> c16(MARK(hd(adx(tl(incr(cons(y0, y1))))))) MARK(hd(hd(adx(tl(incr(s(y0))))))) -> c16(MARK(hd(adx(tl(incr(s(y0))))))) MARK(hd(hd(adx(tl(incr(y0)))))) -> c16(MARK(hd(adx(tl(incr(y0)))))) MARK(hd(hd(adx(tl(hd(nats)))))) -> c16(MARK(hd(adx(tl(hd(nats)))))) MARK(hd(hd(adx(tl(hd(adx(y0))))))) -> c16(MARK(hd(adx(tl(hd(adx(y0))))))) MARK(hd(hd(adx(tl(hd(incr(y0))))))) -> c16(MARK(hd(adx(tl(hd(incr(y0))))))) MARK(hd(hd(adx(tl(hd(hd(y0))))))) -> c16(MARK(hd(adx(tl(hd(hd(y0))))))) MARK(hd(hd(adx(tl(hd(tl(y0))))))) -> c16(MARK(hd(adx(tl(hd(tl(y0))))))) MARK(hd(hd(adx(tl(hd(cons(y0, y1))))))) -> c16(MARK(hd(adx(tl(hd(cons(y0, y1))))))) MARK(hd(hd(adx(tl(hd(y0)))))) -> c16(MARK(hd(adx(tl(hd(y0)))))) MARK(hd(hd(adx(tl(tl(nats)))))) -> c16(MARK(hd(adx(tl(tl(nats)))))) MARK(hd(hd(adx(tl(tl(adx(y0))))))) -> c16(MARK(hd(adx(tl(tl(adx(y0))))))) MARK(hd(hd(adx(tl(tl(incr(y0))))))) -> c16(MARK(hd(adx(tl(tl(incr(y0))))))) MARK(hd(hd(adx(tl(tl(hd(y0))))))) -> c16(MARK(hd(adx(tl(tl(hd(y0))))))) MARK(hd(hd(adx(tl(tl(tl(y0))))))) -> c16(MARK(hd(adx(tl(tl(tl(y0))))))) MARK(hd(hd(adx(tl(tl(cons(y0, y1))))))) -> c16(MARK(hd(adx(tl(tl(cons(y0, y1))))))) MARK(hd(hd(adx(tl(tl(y0)))))) -> c16(MARK(hd(adx(tl(tl(y0)))))) MARK(hd(hd(adx(tl(nats))))) -> c16(MARK(hd(adx(tl(nats))))) MARK(hd(hd(adx(hd(adx(0)))))) -> c16(MARK(hd(adx(hd(adx(0)))))) MARK(hd(hd(adx(hd(adx(s(y0))))))) -> c16(MARK(hd(adx(hd(adx(s(y0))))))) MARK(hd(hd(adx(hd(incr(0)))))) -> c16(MARK(hd(adx(hd(incr(0)))))) MARK(hd(hd(adx(hd(incr(s(y0))))))) -> c16(MARK(hd(adx(hd(incr(s(y0))))))) MARK(hd(hd(adx(hd(hd(zeros)))))) -> c16(MARK(hd(adx(hd(hd(zeros)))))) MARK(hd(hd(adx(tl(hd(zeros)))))) -> c16(MARK(hd(adx(tl(hd(zeros)))))) MARK(hd(hd(adx(tl(adx(0)))))) -> c16(MARK(hd(adx(tl(adx(0)))))) MARK(hd(hd(adx(hd(tl(zeros)))))) -> c16(MARK(hd(adx(hd(tl(zeros)))))) MARK(hd(hd(adx(tl(tl(zeros)))))) -> c16(MARK(hd(adx(tl(tl(zeros)))))) MARK(hd(hd(adx(tl(adx(s(y0))))))) -> c16(MARK(hd(adx(tl(adx(s(y0))))))) MARK(hd(hd(adx(tl(incr(0)))))) -> c16(MARK(hd(adx(tl(incr(0)))))) MARK(hd(hd(incr(hd(cons(y0, y1)))))) -> c16(MARK(hd(incr(hd(cons(y0, y1)))))) MARK(hd(hd(incr(tl(cons(y0, y1)))))) -> c16(MARK(hd(incr(tl(cons(y0, y1)))))) MARK(hd(hd(incr(hd(adx(adx(y0))))))) -> c16(MARK(hd(incr(hd(adx(adx(y0))))))) MARK(hd(hd(incr(hd(adx(incr(y0))))))) -> c16(MARK(hd(incr(hd(adx(incr(y0))))))) MARK(hd(hd(incr(hd(adx(hd(y0))))))) -> c16(MARK(hd(incr(hd(adx(hd(y0))))))) MARK(hd(hd(incr(hd(adx(tl(y0))))))) -> c16(MARK(hd(incr(hd(adx(tl(y0))))))) MARK(hd(hd(incr(hd(adx(y0)))))) -> c16(MARK(hd(incr(hd(adx(y0)))))) MARK(hd(hd(incr(hd(incr(nats)))))) -> c16(MARK(hd(incr(hd(incr(nats)))))) MARK(hd(hd(incr(hd(incr(adx(y0))))))) -> c16(MARK(hd(incr(hd(incr(adx(y0))))))) MARK(hd(hd(incr(hd(incr(zeros)))))) -> c16(MARK(hd(incr(hd(incr(zeros)))))) MARK(hd(hd(incr(hd(incr(incr(y0))))))) -> c16(MARK(hd(incr(hd(incr(incr(y0))))))) MARK(hd(hd(incr(hd(incr(hd(y0))))))) -> c16(MARK(hd(incr(hd(incr(hd(y0))))))) MARK(hd(hd(incr(hd(incr(tl(y0))))))) -> c16(MARK(hd(incr(hd(incr(tl(y0))))))) MARK(hd(hd(incr(hd(incr(cons(y0, y1))))))) -> c16(MARK(hd(incr(hd(incr(cons(y0, y1))))))) MARK(hd(hd(incr(hd(incr(y0)))))) -> c16(MARK(hd(incr(hd(incr(y0)))))) MARK(hd(hd(incr(hd(hd(nats)))))) -> c16(MARK(hd(incr(hd(hd(nats)))))) MARK(hd(hd(incr(hd(hd(adx(y0))))))) -> c16(MARK(hd(incr(hd(hd(adx(y0))))))) MARK(hd(hd(incr(hd(hd(incr(y0))))))) -> c16(MARK(hd(incr(hd(hd(incr(y0))))))) MARK(hd(hd(incr(hd(hd(hd(y0))))))) -> c16(MARK(hd(incr(hd(hd(hd(y0))))))) MARK(hd(hd(incr(hd(hd(tl(y0))))))) -> c16(MARK(hd(incr(hd(hd(tl(y0))))))) MARK(hd(hd(incr(hd(hd(cons(y0, y1))))))) -> c16(MARK(hd(incr(hd(hd(cons(y0, y1))))))) MARK(hd(hd(incr(hd(hd(y0)))))) -> c16(MARK(hd(incr(hd(hd(y0)))))) MARK(hd(hd(incr(hd(tl(nats)))))) -> c16(MARK(hd(incr(hd(tl(nats)))))) MARK(hd(hd(incr(hd(tl(adx(y0))))))) -> c16(MARK(hd(incr(hd(tl(adx(y0))))))) MARK(hd(hd(incr(hd(tl(incr(y0))))))) -> c16(MARK(hd(incr(hd(tl(incr(y0))))))) MARK(hd(hd(incr(hd(tl(hd(y0))))))) -> c16(MARK(hd(incr(hd(tl(hd(y0))))))) MARK(hd(hd(incr(hd(tl(tl(y0))))))) -> c16(MARK(hd(incr(hd(tl(tl(y0))))))) MARK(hd(hd(incr(hd(tl(cons(y0, y1))))))) -> c16(MARK(hd(incr(hd(tl(cons(y0, y1))))))) MARK(hd(hd(incr(hd(tl(y0)))))) -> c16(MARK(hd(incr(hd(tl(y0)))))) MARK(hd(hd(incr(hd(nats))))) -> c16(MARK(hd(incr(hd(nats))))) MARK(hd(hd(incr(tl(adx(adx(y0))))))) -> c16(MARK(hd(incr(tl(adx(adx(y0))))))) MARK(hd(hd(incr(tl(adx(incr(y0))))))) -> c16(MARK(hd(incr(tl(adx(incr(y0))))))) MARK(hd(hd(incr(tl(adx(hd(y0))))))) -> c16(MARK(hd(incr(tl(adx(hd(y0))))))) MARK(hd(hd(incr(tl(adx(tl(y0))))))) -> c16(MARK(hd(incr(tl(adx(tl(y0))))))) MARK(hd(hd(incr(tl(adx(y0)))))) -> c16(MARK(hd(incr(tl(adx(y0)))))) MARK(hd(hd(incr(tl(incr(nats)))))) -> c16(MARK(hd(incr(tl(incr(nats)))))) MARK(hd(hd(incr(tl(incr(adx(y0))))))) -> c16(MARK(hd(incr(tl(incr(adx(y0))))))) MARK(hd(hd(incr(tl(incr(zeros)))))) -> c16(MARK(hd(incr(tl(incr(zeros)))))) MARK(hd(hd(incr(tl(incr(incr(y0))))))) -> c16(MARK(hd(incr(tl(incr(incr(y0))))))) MARK(hd(hd(incr(tl(incr(hd(y0))))))) -> c16(MARK(hd(incr(tl(incr(hd(y0))))))) MARK(hd(hd(incr(tl(incr(tl(y0))))))) -> c16(MARK(hd(incr(tl(incr(tl(y0))))))) MARK(hd(hd(incr(tl(incr(cons(y0, y1))))))) -> c16(MARK(hd(incr(tl(incr(cons(y0, y1))))))) MARK(hd(hd(incr(tl(incr(y0)))))) -> c16(MARK(hd(incr(tl(incr(y0)))))) MARK(hd(hd(incr(tl(hd(nats)))))) -> c16(MARK(hd(incr(tl(hd(nats)))))) MARK(hd(hd(incr(tl(hd(adx(y0))))))) -> c16(MARK(hd(incr(tl(hd(adx(y0))))))) MARK(hd(hd(incr(tl(hd(incr(y0))))))) -> c16(MARK(hd(incr(tl(hd(incr(y0))))))) MARK(hd(hd(incr(tl(hd(hd(y0))))))) -> c16(MARK(hd(incr(tl(hd(hd(y0))))))) MARK(hd(hd(incr(tl(hd(tl(y0))))))) -> c16(MARK(hd(incr(tl(hd(tl(y0))))))) MARK(hd(hd(incr(tl(hd(cons(y0, y1))))))) -> c16(MARK(hd(incr(tl(hd(cons(y0, y1))))))) MARK(hd(hd(incr(tl(hd(y0)))))) -> c16(MARK(hd(incr(tl(hd(y0)))))) MARK(hd(hd(incr(tl(tl(nats)))))) -> c16(MARK(hd(incr(tl(tl(nats)))))) MARK(hd(hd(incr(tl(tl(adx(y0))))))) -> c16(MARK(hd(incr(tl(tl(adx(y0))))))) MARK(hd(hd(incr(tl(tl(incr(y0))))))) -> c16(MARK(hd(incr(tl(tl(incr(y0))))))) MARK(hd(hd(incr(tl(tl(hd(y0))))))) -> c16(MARK(hd(incr(tl(tl(hd(y0))))))) MARK(hd(hd(incr(tl(tl(tl(y0))))))) -> c16(MARK(hd(incr(tl(tl(tl(y0))))))) MARK(hd(hd(incr(tl(tl(cons(y0, y1))))))) -> c16(MARK(hd(incr(tl(tl(cons(y0, y1))))))) MARK(hd(hd(incr(tl(tl(y0)))))) -> c16(MARK(hd(incr(tl(tl(y0)))))) MARK(hd(hd(incr(tl(nats))))) -> c16(MARK(hd(incr(tl(nats))))) MARK(hd(hd(incr(hd(incr(0)))))) -> c16(MARK(hd(incr(hd(incr(0)))))) MARK(hd(hd(incr(hd(incr(s(y0))))))) -> c16(MARK(hd(incr(hd(incr(s(y0))))))) MARK(hd(hd(incr(hd(hd(zeros)))))) -> c16(MARK(hd(incr(hd(hd(zeros)))))) MARK(hd(hd(incr(tl(hd(zeros)))))) -> c16(MARK(hd(incr(tl(hd(zeros)))))) MARK(hd(hd(incr(hd(tl(zeros)))))) -> c16(MARK(hd(incr(hd(tl(zeros)))))) MARK(hd(hd(incr(tl(tl(zeros)))))) -> c16(MARK(hd(incr(tl(tl(zeros)))))) MARK(hd(hd(incr(tl(incr(0)))))) -> c16(MARK(hd(incr(tl(incr(0)))))) MARK(hd(hd(incr(adx(adx(y0)))))) -> c16(MARK(hd(incr(adx(adx(y0)))))) MARK(hd(hd(incr(adx(incr(y0)))))) -> c16(MARK(hd(incr(adx(incr(y0)))))) MARK(hd(hd(incr(adx(hd(cons(y0, y1))))))) -> c16(MARK(hd(incr(adx(hd(cons(y0, y1))))))) MARK(hd(hd(incr(adx(tl(cons(y0, y1))))))) -> c16(MARK(hd(incr(adx(tl(cons(y0, y1))))))) MARK(hd(hd(incr(adx(hd(adx(nats))))))) -> c16(MARK(hd(incr(adx(hd(adx(nats))))))) MARK(hd(hd(incr(adx(hd(adx(adx(y0)))))))) -> c16(MARK(hd(incr(adx(hd(adx(adx(y0)))))))) MARK(hd(hd(incr(adx(hd(adx(zeros))))))) -> c16(MARK(hd(incr(adx(hd(adx(zeros))))))) MARK(hd(hd(incr(adx(hd(adx(incr(y0)))))))) -> c16(MARK(hd(incr(adx(hd(adx(incr(y0)))))))) MARK(hd(hd(incr(adx(hd(adx(hd(y0)))))))) -> c16(MARK(hd(incr(adx(hd(adx(hd(y0)))))))) MARK(hd(hd(incr(adx(hd(adx(tl(y0)))))))) -> c16(MARK(hd(incr(adx(hd(adx(tl(y0)))))))) MARK(hd(hd(incr(adx(hd(adx(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(hd(adx(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(hd(adx(y0))))))) -> c16(MARK(hd(incr(adx(hd(adx(y0))))))) MARK(hd(hd(incr(adx(hd(incr(nats))))))) -> c16(MARK(hd(incr(adx(hd(incr(nats))))))) MARK(hd(hd(incr(adx(hd(incr(adx(y0)))))))) -> c16(MARK(hd(incr(adx(hd(incr(adx(y0)))))))) MARK(hd(hd(incr(adx(hd(incr(zeros))))))) -> c16(MARK(hd(incr(adx(hd(incr(zeros))))))) MARK(hd(hd(incr(adx(hd(incr(incr(y0)))))))) -> c16(MARK(hd(incr(adx(hd(incr(incr(y0)))))))) MARK(hd(hd(incr(adx(hd(incr(hd(y0)))))))) -> c16(MARK(hd(incr(adx(hd(incr(hd(y0)))))))) MARK(hd(hd(incr(adx(hd(incr(tl(y0)))))))) -> c16(MARK(hd(incr(adx(hd(incr(tl(y0)))))))) MARK(hd(hd(incr(adx(hd(incr(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(hd(incr(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(hd(incr(y0))))))) -> c16(MARK(hd(incr(adx(hd(incr(y0))))))) MARK(hd(hd(incr(adx(hd(hd(nats))))))) -> c16(MARK(hd(incr(adx(hd(hd(nats))))))) MARK(hd(hd(incr(adx(hd(hd(adx(y0)))))))) -> c16(MARK(hd(incr(adx(hd(hd(adx(y0)))))))) MARK(hd(hd(incr(adx(hd(hd(incr(y0)))))))) -> c16(MARK(hd(incr(adx(hd(hd(incr(y0)))))))) MARK(hd(hd(incr(adx(hd(hd(hd(y0)))))))) -> c16(MARK(hd(incr(adx(hd(hd(hd(y0)))))))) MARK(hd(hd(incr(adx(hd(hd(tl(y0)))))))) -> c16(MARK(hd(incr(adx(hd(hd(tl(y0)))))))) MARK(hd(hd(incr(adx(hd(hd(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(hd(hd(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(hd(hd(y0))))))) -> c16(MARK(hd(incr(adx(hd(hd(y0))))))) MARK(hd(hd(incr(adx(hd(tl(nats))))))) -> c16(MARK(hd(incr(adx(hd(tl(nats))))))) MARK(hd(hd(incr(adx(hd(tl(adx(y0)))))))) -> c16(MARK(hd(incr(adx(hd(tl(adx(y0)))))))) MARK(hd(hd(incr(adx(hd(tl(incr(y0)))))))) -> c16(MARK(hd(incr(adx(hd(tl(incr(y0)))))))) MARK(hd(hd(incr(adx(hd(tl(hd(y0)))))))) -> c16(MARK(hd(incr(adx(hd(tl(hd(y0)))))))) MARK(hd(hd(incr(adx(hd(tl(tl(y0)))))))) -> c16(MARK(hd(incr(adx(hd(tl(tl(y0)))))))) MARK(hd(hd(incr(adx(hd(tl(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(hd(tl(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(hd(tl(y0))))))) -> c16(MARK(hd(incr(adx(hd(tl(y0))))))) MARK(hd(hd(incr(adx(hd(nats)))))) -> c16(MARK(hd(incr(adx(hd(nats)))))) MARK(hd(hd(incr(adx(tl(adx(nats))))))) -> c16(MARK(hd(incr(adx(tl(adx(nats))))))) MARK(hd(hd(incr(adx(tl(adx(adx(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(adx(y0)))))))) MARK(hd(hd(incr(adx(tl(adx(zeros))))))) -> c16(MARK(hd(incr(adx(tl(adx(zeros))))))) MARK(hd(hd(incr(adx(tl(adx(incr(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(incr(y0)))))))) MARK(hd(hd(incr(adx(tl(adx(hd(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(hd(y0)))))))) MARK(hd(hd(incr(adx(tl(adx(tl(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(tl(y0)))))))) MARK(hd(hd(incr(adx(tl(adx(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(tl(adx(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(tl(adx(y0))))))) -> c16(MARK(hd(incr(adx(tl(adx(y0))))))) MARK(hd(hd(incr(adx(tl(incr(nats))))))) -> c16(MARK(hd(incr(adx(tl(incr(nats))))))) MARK(hd(hd(incr(adx(tl(incr(adx(y0)))))))) -> c16(MARK(hd(incr(adx(tl(incr(adx(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(zeros))))))) -> c16(MARK(hd(incr(adx(tl(incr(zeros))))))) MARK(hd(hd(incr(adx(tl(incr(incr(y0)))))))) -> c16(MARK(hd(incr(adx(tl(incr(incr(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(hd(y0)))))))) -> c16(MARK(hd(incr(adx(tl(incr(hd(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(tl(y0)))))))) -> c16(MARK(hd(incr(adx(tl(incr(tl(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(tl(incr(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(tl(incr(s(y0)))))))) -> c16(MARK(hd(incr(adx(tl(incr(s(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(y0))))))) -> c16(MARK(hd(incr(adx(tl(incr(y0))))))) MARK(hd(hd(incr(adx(tl(hd(nats))))))) -> c16(MARK(hd(incr(adx(tl(hd(nats))))))) MARK(hd(hd(incr(adx(tl(hd(adx(y0)))))))) -> c16(MARK(hd(incr(adx(tl(hd(adx(y0)))))))) MARK(hd(hd(incr(adx(tl(hd(incr(y0)))))))) -> c16(MARK(hd(incr(adx(tl(hd(incr(y0)))))))) MARK(hd(hd(incr(adx(tl(hd(hd(y0)))))))) -> c16(MARK(hd(incr(adx(tl(hd(hd(y0)))))))) MARK(hd(hd(incr(adx(tl(hd(tl(y0)))))))) -> c16(MARK(hd(incr(adx(tl(hd(tl(y0)))))))) MARK(hd(hd(incr(adx(tl(hd(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(tl(hd(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(tl(hd(y0))))))) -> c16(MARK(hd(incr(adx(tl(hd(y0))))))) MARK(hd(hd(incr(adx(tl(tl(nats))))))) -> c16(MARK(hd(incr(adx(tl(tl(nats))))))) MARK(hd(hd(incr(adx(tl(tl(adx(y0)))))))) -> c16(MARK(hd(incr(adx(tl(tl(adx(y0)))))))) MARK(hd(hd(incr(adx(tl(tl(incr(y0)))))))) -> c16(MARK(hd(incr(adx(tl(tl(incr(y0)))))))) MARK(hd(hd(incr(adx(tl(tl(hd(y0)))))))) -> c16(MARK(hd(incr(adx(tl(tl(hd(y0)))))))) MARK(hd(hd(incr(adx(tl(tl(tl(y0)))))))) -> c16(MARK(hd(incr(adx(tl(tl(tl(y0)))))))) MARK(hd(hd(incr(adx(tl(tl(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(tl(tl(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(tl(tl(y0))))))) -> c16(MARK(hd(incr(adx(tl(tl(y0))))))) MARK(hd(hd(incr(adx(tl(nats)))))) -> c16(MARK(hd(incr(adx(tl(nats)))))) MARK(hd(hd(incr(adx(hd(adx(0))))))) -> c16(MARK(hd(incr(adx(hd(adx(0))))))) MARK(hd(hd(incr(adx(hd(adx(s(y0)))))))) -> c16(MARK(hd(incr(adx(hd(adx(s(y0)))))))) MARK(hd(hd(incr(adx(hd(incr(0))))))) -> c16(MARK(hd(incr(adx(hd(incr(0))))))) MARK(hd(hd(incr(adx(hd(incr(s(y0)))))))) -> c16(MARK(hd(incr(adx(hd(incr(s(y0)))))))) MARK(hd(hd(incr(adx(hd(hd(zeros))))))) -> c16(MARK(hd(incr(adx(hd(hd(zeros))))))) MARK(hd(hd(incr(adx(tl(hd(zeros))))))) -> c16(MARK(hd(incr(adx(tl(hd(zeros))))))) MARK(hd(hd(incr(adx(tl(adx(0))))))) -> c16(MARK(hd(incr(adx(tl(adx(0))))))) MARK(hd(hd(incr(adx(hd(tl(zeros))))))) -> c16(MARK(hd(incr(adx(hd(tl(zeros))))))) MARK(hd(hd(incr(adx(tl(tl(zeros))))))) -> c16(MARK(hd(incr(adx(tl(tl(zeros))))))) MARK(hd(hd(incr(adx(tl(adx(s(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(s(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(0))))))) -> c16(MARK(hd(incr(adx(tl(incr(0))))))) MARK(hd(hd(incr(hd(adx(nats)))))) -> c16(MARK(hd(incr(hd(adx(nats)))))) MARK(hd(hd(incr(hd(adx(zeros)))))) -> c16(MARK(hd(incr(hd(adx(zeros)))))) MARK(hd(hd(incr(hd(adx(cons(y0, y1))))))) -> c16(MARK(hd(incr(hd(adx(cons(y0, y1))))))) MARK(hd(hd(incr(tl(adx(nats)))))) -> c16(MARK(hd(incr(tl(adx(nats)))))) MARK(hd(hd(incr(tl(adx(zeros)))))) -> c16(MARK(hd(incr(tl(adx(zeros)))))) MARK(hd(hd(incr(tl(adx(cons(y0, y1))))))) -> c16(MARK(hd(incr(tl(adx(cons(y0, y1))))))) MARK(hd(hd(incr(tl(incr(s(y0))))))) -> c16(MARK(hd(incr(tl(incr(s(y0))))))) S tuples: MARK(hd(adx(adx(z0)))) -> c16(A__HD(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(hd(adx(incr(z0)))) -> c16(A__HD(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(hd(adx(hd(z0)))) -> c16(A__HD(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(hd(adx(tl(z0)))) -> c16(A__HD(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(hd(incr(adx(z0)))) -> c16(A__HD(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(hd(incr(incr(z0)))) -> c16(A__HD(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(hd(incr(hd(z0)))) -> c16(A__HD(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(hd(incr(tl(z0)))) -> c16(A__HD(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(hd(hd(nats))) -> c16(A__HD(a__hd(a__nats)), MARK(hd(nats))) MARK(hd(hd(adx(z0)))) -> c16(A__HD(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(hd(hd(incr(z0)))) -> c16(A__HD(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(hd(hd(hd(z0)))) -> c16(A__HD(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(hd(hd(tl(z0)))) -> c16(A__HD(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(hd(hd(cons(z0, z1)))) -> c16(A__HD(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(hd(tl(nats))) -> c16(A__HD(a__tl(a__nats)), MARK(tl(nats))) MARK(hd(tl(adx(z0)))) -> c16(A__HD(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(hd(tl(incr(z0)))) -> c16(A__HD(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(hd(tl(hd(z0)))) -> c16(A__HD(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(hd(tl(tl(z0)))) -> c16(A__HD(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(hd(tl(cons(z0, z1)))) -> c16(A__HD(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(hd(tl(x0))) -> c16(MARK(tl(x0))) MARK(hd(nats)) -> c16(A__HD(a__adx(a__zeros))) MARK(tl(adx(adx(z0)))) -> c17(A__TL(a__adx(a__adx(mark(z0)))), MARK(adx(adx(z0)))) MARK(tl(adx(incr(z0)))) -> c17(A__TL(a__adx(a__incr(mark(z0)))), MARK(adx(incr(z0)))) MARK(tl(adx(hd(z0)))) -> c17(A__TL(a__adx(a__hd(mark(z0)))), MARK(adx(hd(z0)))) MARK(tl(adx(tl(z0)))) -> c17(A__TL(a__adx(a__tl(mark(z0)))), MARK(adx(tl(z0)))) MARK(tl(adx(x0))) -> c17(MARK(adx(x0))) MARK(tl(incr(adx(z0)))) -> c17(A__TL(a__incr(a__adx(mark(z0)))), MARK(incr(adx(z0)))) MARK(tl(incr(incr(z0)))) -> c17(A__TL(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(tl(incr(hd(z0)))) -> c17(A__TL(a__incr(a__hd(mark(z0)))), MARK(incr(hd(z0)))) MARK(tl(incr(tl(z0)))) -> c17(A__TL(a__incr(a__tl(mark(z0)))), MARK(incr(tl(z0)))) MARK(tl(incr(x0))) -> c17(MARK(incr(x0))) MARK(tl(hd(nats))) -> c17(A__TL(a__hd(a__nats)), MARK(hd(nats))) MARK(tl(hd(adx(z0)))) -> c17(A__TL(a__hd(a__adx(mark(z0)))), MARK(hd(adx(z0)))) MARK(tl(hd(incr(z0)))) -> c17(A__TL(a__hd(a__incr(mark(z0)))), MARK(hd(incr(z0)))) MARK(tl(hd(hd(z0)))) -> c17(A__TL(a__hd(a__hd(mark(z0)))), MARK(hd(hd(z0)))) MARK(tl(hd(tl(z0)))) -> c17(A__TL(a__hd(a__tl(mark(z0)))), MARK(hd(tl(z0)))) MARK(tl(hd(cons(z0, z1)))) -> c17(A__TL(a__hd(cons(z0, z1))), MARK(hd(cons(z0, z1)))) MARK(tl(hd(x0))) -> c17(MARK(hd(x0))) MARK(tl(tl(nats))) -> c17(A__TL(a__tl(a__nats)), MARK(tl(nats))) MARK(tl(tl(adx(z0)))) -> c17(A__TL(a__tl(a__adx(mark(z0)))), MARK(tl(adx(z0)))) MARK(tl(tl(incr(z0)))) -> c17(A__TL(a__tl(a__incr(mark(z0)))), MARK(tl(incr(z0)))) MARK(tl(tl(hd(z0)))) -> c17(A__TL(a__tl(a__hd(mark(z0)))), MARK(tl(hd(z0)))) MARK(tl(tl(tl(z0)))) -> c17(A__TL(a__tl(a__tl(mark(z0)))), MARK(tl(tl(z0)))) MARK(tl(tl(cons(z0, z1)))) -> c17(A__TL(a__tl(cons(z0, z1))), MARK(tl(cons(z0, z1)))) MARK(tl(tl(x0))) -> c17(MARK(tl(x0))) 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MARK(adx(hd(incr(adx(y0))))) -> c13(MARK(hd(incr(adx(y0))))) MARK(adx(hd(incr(zeros)))) -> c13(MARK(hd(incr(zeros)))) MARK(adx(hd(incr(incr(y0))))) -> c13(MARK(hd(incr(incr(y0))))) MARK(adx(hd(incr(hd(y0))))) -> c13(MARK(hd(incr(hd(y0))))) MARK(adx(hd(incr(tl(y0))))) -> c13(MARK(hd(incr(tl(y0))))) MARK(adx(hd(incr(y0)))) -> c13(MARK(hd(incr(y0)))) MARK(adx(hd(hd(nats)))) -> c13(MARK(hd(hd(nats)))) MARK(adx(hd(hd(adx(y0))))) -> c13(MARK(hd(hd(adx(y0))))) MARK(adx(hd(hd(incr(y0))))) -> c13(MARK(hd(hd(incr(y0))))) MARK(adx(hd(hd(hd(y0))))) -> c13(MARK(hd(hd(hd(y0))))) MARK(adx(hd(hd(tl(y0))))) -> c13(MARK(hd(hd(tl(y0))))) MARK(adx(hd(hd(cons(y0, y1))))) -> c13(MARK(hd(hd(cons(y0, y1))))) MARK(adx(hd(hd(y0)))) -> c13(MARK(hd(hd(y0)))) MARK(adx(hd(tl(nats)))) -> c13(MARK(hd(tl(nats)))) MARK(adx(hd(tl(adx(y0))))) -> c13(MARK(hd(tl(adx(y0))))) MARK(adx(hd(tl(incr(y0))))) -> c13(MARK(hd(tl(incr(y0))))) MARK(adx(hd(tl(hd(y0))))) -> c13(MARK(hd(tl(hd(y0))))) MARK(adx(hd(tl(tl(y0))))) -> c13(MARK(hd(tl(tl(y0))))) MARK(adx(hd(tl(cons(y0, y1))))) -> c13(MARK(hd(tl(cons(y0, y1))))) MARK(adx(hd(tl(y0)))) -> c13(MARK(hd(tl(y0)))) MARK(adx(hd(nats))) -> c13(MARK(hd(nats))) MARK(adx(tl(adx(nats)))) -> c13(MARK(tl(adx(nats)))) MARK(adx(tl(adx(adx(y0))))) -> c13(MARK(tl(adx(adx(y0))))) MARK(adx(tl(adx(zeros)))) -> c13(MARK(tl(adx(zeros)))) MARK(adx(tl(adx(incr(y0))))) -> c13(MARK(tl(adx(incr(y0))))) MARK(adx(tl(adx(hd(y0))))) -> c13(MARK(tl(adx(hd(y0))))) MARK(adx(tl(adx(tl(y0))))) -> c13(MARK(tl(adx(tl(y0))))) MARK(adx(tl(adx(cons(y0, y1))))) -> c13(MARK(tl(adx(cons(y0, y1))))) MARK(adx(tl(adx(y0)))) -> c13(MARK(tl(adx(y0)))) MARK(adx(tl(incr(nats)))) -> c13(MARK(tl(incr(nats)))) MARK(adx(tl(incr(adx(y0))))) -> c13(MARK(tl(incr(adx(y0))))) MARK(adx(tl(incr(zeros)))) -> c13(MARK(tl(incr(zeros)))) MARK(adx(tl(incr(incr(y0))))) -> c13(MARK(tl(incr(incr(y0))))) MARK(adx(tl(incr(hd(y0))))) -> c13(MARK(tl(incr(hd(y0))))) MARK(adx(tl(incr(tl(y0))))) -> c13(MARK(tl(incr(tl(y0))))) MARK(adx(tl(incr(cons(y0, y1))))) -> c13(MARK(tl(incr(cons(y0, y1))))) MARK(adx(tl(incr(s(y0))))) -> c13(MARK(tl(incr(s(y0))))) MARK(adx(tl(incr(y0)))) -> c13(MARK(tl(incr(y0)))) MARK(adx(tl(hd(nats)))) -> c13(MARK(tl(hd(nats)))) MARK(adx(tl(hd(adx(y0))))) -> c13(MARK(tl(hd(adx(y0))))) MARK(adx(tl(hd(incr(y0))))) -> c13(MARK(tl(hd(incr(y0))))) MARK(adx(tl(hd(hd(y0))))) -> c13(MARK(tl(hd(hd(y0))))) MARK(adx(tl(hd(tl(y0))))) -> c13(MARK(tl(hd(tl(y0))))) MARK(adx(tl(hd(cons(y0, y1))))) -> c13(MARK(tl(hd(cons(y0, y1))))) MARK(adx(tl(hd(y0)))) -> c13(MARK(tl(hd(y0)))) MARK(adx(tl(tl(nats)))) -> c13(MARK(tl(tl(nats)))) MARK(adx(tl(tl(adx(y0))))) -> c13(MARK(tl(tl(adx(y0))))) MARK(adx(tl(tl(incr(y0))))) -> c13(MARK(tl(tl(incr(y0))))) MARK(adx(tl(tl(hd(y0))))) -> c13(MARK(tl(tl(hd(y0))))) MARK(adx(tl(tl(tl(y0))))) -> c13(MARK(tl(tl(tl(y0))))) MARK(adx(tl(tl(cons(y0, y1))))) -> c13(MARK(tl(tl(cons(y0, y1))))) MARK(adx(tl(tl(y0)))) -> c13(MARK(tl(tl(y0)))) MARK(adx(tl(nats))) -> c13(MARK(tl(nats))) MARK(adx(hd(hd(zeros)))) -> c13(MARK(hd(hd(zeros)))) MARK(adx(tl(hd(zeros)))) -> c13(MARK(tl(hd(zeros)))) MARK(adx(tl(adx(0)))) -> c13(MARK(tl(adx(0)))) MARK(adx(hd(tl(zeros)))) -> c13(MARK(hd(tl(zeros)))) MARK(adx(tl(tl(zeros)))) -> c13(MARK(tl(tl(zeros)))) MARK(adx(tl(adx(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) MARK(adx(tl(incr(0)))) -> c13(MARK(tl(incr(0)))) MARK(hd(adx(nats))) -> c16(A__HD(a__adx(a__nats))) MARK(hd(adx(zeros))) -> c16(A__HD(a__adx(a__zeros))) MARK(hd(adx(cons(z0, z1)))) -> c16(A__HD(a__adx(cons(z0, z1)))) MARK(tl(adx(nats))) -> c17(A__TL(a__adx(a__nats))) MARK(tl(adx(zeros))) -> c17(A__TL(a__adx(a__zeros))) MARK(tl(adx(cons(z0, z1)))) -> c17(A__TL(a__adx(cons(z0, z1)))) MARK(incr(incr(y0))) -> c15(MARK(incr(y0))) MARK(incr(hd(cons(y0, y1)))) -> c15(MARK(hd(cons(y0, y1)))) MARK(incr(tl(cons(y0, y1)))) -> c15(MARK(tl(cons(y0, y1)))) MARK(incr(hd(adx(adx(y0))))) -> c15(MARK(hd(adx(adx(y0))))) MARK(incr(hd(adx(incr(y0))))) -> c15(MARK(hd(adx(incr(y0))))) MARK(incr(hd(adx(hd(y0))))) -> c15(MARK(hd(adx(hd(y0))))) MARK(incr(hd(adx(tl(y0))))) -> c15(MARK(hd(adx(tl(y0))))) MARK(incr(hd(adx(y0)))) -> c15(MARK(hd(adx(y0)))) MARK(incr(hd(incr(nats)))) -> c15(MARK(hd(incr(nats)))) MARK(incr(hd(incr(adx(y0))))) -> c15(MARK(hd(incr(adx(y0))))) MARK(incr(hd(incr(zeros)))) -> c15(MARK(hd(incr(zeros)))) MARK(incr(hd(incr(incr(y0))))) -> c15(MARK(hd(incr(incr(y0))))) MARK(incr(hd(incr(hd(y0))))) -> c15(MARK(hd(incr(hd(y0))))) MARK(incr(hd(incr(tl(y0))))) -> c15(MARK(hd(incr(tl(y0))))) MARK(incr(hd(incr(y0)))) -> c15(MARK(hd(incr(y0)))) MARK(incr(hd(hd(nats)))) -> c15(MARK(hd(hd(nats)))) MARK(incr(hd(hd(adx(y0))))) -> c15(MARK(hd(hd(adx(y0))))) MARK(incr(hd(hd(incr(y0))))) -> c15(MARK(hd(hd(incr(y0))))) MARK(incr(hd(hd(hd(y0))))) -> c15(MARK(hd(hd(hd(y0))))) MARK(incr(hd(hd(tl(y0))))) -> c15(MARK(hd(hd(tl(y0))))) MARK(incr(hd(hd(cons(y0, y1))))) -> c15(MARK(hd(hd(cons(y0, y1))))) MARK(incr(hd(hd(y0)))) -> c15(MARK(hd(hd(y0)))) MARK(incr(hd(tl(nats)))) -> c15(MARK(hd(tl(nats)))) MARK(incr(hd(tl(adx(y0))))) -> c15(MARK(hd(tl(adx(y0))))) MARK(incr(hd(tl(incr(y0))))) -> c15(MARK(hd(tl(incr(y0))))) MARK(incr(hd(tl(hd(y0))))) -> c15(MARK(hd(tl(hd(y0))))) MARK(incr(hd(tl(tl(y0))))) -> c15(MARK(hd(tl(tl(y0))))) MARK(incr(hd(tl(cons(y0, y1))))) -> c15(MARK(hd(tl(cons(y0, y1))))) MARK(incr(hd(tl(y0)))) -> c15(MARK(hd(tl(y0)))) MARK(incr(hd(nats))) -> c15(MARK(hd(nats))) MARK(incr(tl(adx(adx(y0))))) -> c15(MARK(tl(adx(adx(y0))))) MARK(incr(tl(adx(incr(y0))))) -> c15(MARK(tl(adx(incr(y0))))) MARK(incr(tl(adx(hd(y0))))) -> c15(MARK(tl(adx(hd(y0))))) MARK(incr(tl(adx(tl(y0))))) -> c15(MARK(tl(adx(tl(y0))))) MARK(incr(tl(adx(y0)))) -> c15(MARK(tl(adx(y0)))) MARK(incr(tl(incr(nats)))) -> c15(MARK(tl(incr(nats)))) MARK(incr(tl(incr(adx(y0))))) -> c15(MARK(tl(incr(adx(y0))))) MARK(incr(tl(incr(zeros)))) -> c15(MARK(tl(incr(zeros)))) MARK(incr(tl(incr(incr(y0))))) -> c15(MARK(tl(incr(incr(y0))))) MARK(incr(tl(incr(hd(y0))))) -> c15(MARK(tl(incr(hd(y0))))) MARK(incr(tl(incr(tl(y0))))) -> c15(MARK(tl(incr(tl(y0))))) MARK(incr(tl(incr(cons(y0, y1))))) -> c15(MARK(tl(incr(cons(y0, y1))))) MARK(incr(tl(incr(y0)))) -> c15(MARK(tl(incr(y0)))) MARK(incr(tl(hd(nats)))) -> c15(MARK(tl(hd(nats)))) MARK(incr(tl(hd(adx(y0))))) -> c15(MARK(tl(hd(adx(y0))))) MARK(incr(tl(hd(incr(y0))))) -> c15(MARK(tl(hd(incr(y0))))) MARK(incr(tl(hd(hd(y0))))) -> c15(MARK(tl(hd(hd(y0))))) MARK(incr(tl(hd(tl(y0))))) -> c15(MARK(tl(hd(tl(y0))))) MARK(incr(tl(hd(cons(y0, y1))))) -> c15(MARK(tl(hd(cons(y0, y1))))) MARK(incr(tl(hd(y0)))) -> c15(MARK(tl(hd(y0)))) MARK(incr(tl(tl(nats)))) -> c15(MARK(tl(tl(nats)))) MARK(incr(tl(tl(adx(y0))))) -> c15(MARK(tl(tl(adx(y0))))) MARK(incr(tl(tl(incr(y0))))) -> c15(MARK(tl(tl(incr(y0))))) MARK(incr(tl(tl(hd(y0))))) -> c15(MARK(tl(tl(hd(y0))))) MARK(incr(tl(tl(tl(y0))))) -> c15(MARK(tl(tl(tl(y0))))) MARK(incr(tl(tl(cons(y0, y1))))) -> c15(MARK(tl(tl(cons(y0, y1))))) MARK(incr(tl(tl(y0)))) -> c15(MARK(tl(tl(y0)))) MARK(incr(tl(nats))) -> c15(MARK(tl(nats))) MARK(incr(hd(hd(zeros)))) -> c15(MARK(hd(hd(zeros)))) MARK(incr(tl(hd(zeros)))) -> c15(MARK(tl(hd(zeros)))) MARK(incr(hd(tl(zeros)))) -> c15(MARK(hd(tl(zeros)))) MARK(incr(tl(tl(zeros)))) -> c15(MARK(tl(tl(zeros)))) MARK(incr(tl(incr(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(adx(adx(y0)))) -> c15(MARK(adx(adx(y0)))) MARK(incr(adx(incr(y0)))) -> c15(MARK(adx(incr(y0)))) MARK(incr(adx(hd(cons(y0, y1))))) -> c15(MARK(adx(hd(cons(y0, y1))))) MARK(incr(adx(tl(cons(y0, y1))))) -> c15(MARK(adx(tl(cons(y0, y1))))) MARK(incr(adx(hd(adx(nats))))) -> c15(MARK(adx(hd(adx(nats))))) MARK(incr(adx(hd(adx(adx(y0)))))) -> c15(MARK(adx(hd(adx(adx(y0)))))) MARK(incr(adx(hd(adx(zeros))))) -> c15(MARK(adx(hd(adx(zeros))))) MARK(incr(adx(hd(adx(incr(y0)))))) -> c15(MARK(adx(hd(adx(incr(y0)))))) MARK(incr(adx(hd(adx(hd(y0)))))) -> c15(MARK(adx(hd(adx(hd(y0)))))) MARK(incr(adx(hd(adx(tl(y0)))))) -> c15(MARK(adx(hd(adx(tl(y0)))))) MARK(incr(adx(hd(adx(cons(y0, y1)))))) -> c15(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(incr(adx(hd(adx(y0))))) -> c15(MARK(adx(hd(adx(y0))))) MARK(incr(adx(hd(incr(nats))))) -> c15(MARK(adx(hd(incr(nats))))) MARK(incr(adx(hd(incr(adx(y0)))))) -> c15(MARK(adx(hd(incr(adx(y0)))))) MARK(incr(adx(hd(incr(zeros))))) -> c15(MARK(adx(hd(incr(zeros))))) MARK(incr(adx(hd(incr(incr(y0)))))) -> c15(MARK(adx(hd(incr(incr(y0)))))) MARK(incr(adx(hd(incr(hd(y0)))))) -> c15(MARK(adx(hd(incr(hd(y0)))))) MARK(incr(adx(hd(incr(tl(y0)))))) -> c15(MARK(adx(hd(incr(tl(y0)))))) MARK(incr(adx(hd(incr(cons(y0, y1)))))) -> c15(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(incr(adx(hd(incr(y0))))) -> c15(MARK(adx(hd(incr(y0))))) MARK(incr(adx(hd(hd(nats))))) -> c15(MARK(adx(hd(hd(nats))))) MARK(incr(adx(hd(hd(adx(y0)))))) -> c15(MARK(adx(hd(hd(adx(y0)))))) MARK(incr(adx(hd(hd(incr(y0)))))) -> c15(MARK(adx(hd(hd(incr(y0)))))) MARK(incr(adx(hd(hd(hd(y0)))))) -> c15(MARK(adx(hd(hd(hd(y0)))))) MARK(incr(adx(hd(hd(tl(y0)))))) -> c15(MARK(adx(hd(hd(tl(y0)))))) MARK(incr(adx(hd(hd(cons(y0, y1)))))) -> c15(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(incr(adx(hd(hd(y0))))) -> c15(MARK(adx(hd(hd(y0))))) MARK(incr(adx(hd(tl(nats))))) -> c15(MARK(adx(hd(tl(nats))))) MARK(incr(adx(hd(tl(adx(y0)))))) -> c15(MARK(adx(hd(tl(adx(y0)))))) MARK(incr(adx(hd(tl(incr(y0)))))) -> c15(MARK(adx(hd(tl(incr(y0)))))) MARK(incr(adx(hd(tl(hd(y0)))))) -> c15(MARK(adx(hd(tl(hd(y0)))))) MARK(incr(adx(hd(tl(tl(y0)))))) -> c15(MARK(adx(hd(tl(tl(y0)))))) MARK(incr(adx(hd(tl(cons(y0, y1)))))) -> c15(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(incr(adx(hd(tl(y0))))) -> c15(MARK(adx(hd(tl(y0))))) MARK(incr(adx(hd(nats)))) -> c15(MARK(adx(hd(nats)))) MARK(incr(adx(tl(adx(nats))))) -> c15(MARK(adx(tl(adx(nats))))) MARK(incr(adx(tl(adx(adx(y0)))))) -> c15(MARK(adx(tl(adx(adx(y0)))))) MARK(incr(adx(tl(adx(zeros))))) -> c15(MARK(adx(tl(adx(zeros))))) MARK(incr(adx(tl(adx(incr(y0)))))) -> c15(MARK(adx(tl(adx(incr(y0)))))) MARK(incr(adx(tl(adx(hd(y0)))))) -> c15(MARK(adx(tl(adx(hd(y0)))))) MARK(incr(adx(tl(adx(tl(y0)))))) -> c15(MARK(adx(tl(adx(tl(y0)))))) MARK(incr(adx(tl(adx(cons(y0, y1)))))) -> c15(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(incr(adx(tl(adx(y0))))) -> c15(MARK(adx(tl(adx(y0))))) MARK(incr(adx(tl(incr(nats))))) -> c15(MARK(adx(tl(incr(nats))))) MARK(incr(adx(tl(incr(adx(y0)))))) -> c15(MARK(adx(tl(incr(adx(y0)))))) MARK(incr(adx(tl(incr(zeros))))) -> c15(MARK(adx(tl(incr(zeros))))) MARK(incr(adx(tl(incr(incr(y0)))))) -> c15(MARK(adx(tl(incr(incr(y0)))))) MARK(incr(adx(tl(incr(hd(y0)))))) -> c15(MARK(adx(tl(incr(hd(y0)))))) MARK(incr(adx(tl(incr(tl(y0)))))) -> c15(MARK(adx(tl(incr(tl(y0)))))) MARK(incr(adx(tl(incr(cons(y0, y1)))))) -> c15(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(incr(adx(tl(incr(s(y0)))))) -> c15(MARK(adx(tl(incr(s(y0)))))) MARK(incr(adx(tl(incr(y0))))) -> c15(MARK(adx(tl(incr(y0))))) MARK(incr(adx(tl(hd(nats))))) -> c15(MARK(adx(tl(hd(nats))))) MARK(incr(adx(tl(hd(adx(y0)))))) -> c15(MARK(adx(tl(hd(adx(y0)))))) MARK(incr(adx(tl(hd(incr(y0)))))) -> c15(MARK(adx(tl(hd(incr(y0)))))) MARK(incr(adx(tl(hd(hd(y0)))))) -> c15(MARK(adx(tl(hd(hd(y0)))))) MARK(incr(adx(tl(hd(tl(y0)))))) -> c15(MARK(adx(tl(hd(tl(y0)))))) MARK(incr(adx(tl(hd(cons(y0, y1)))))) -> c15(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(incr(adx(tl(hd(y0))))) -> c15(MARK(adx(tl(hd(y0))))) MARK(incr(adx(tl(tl(nats))))) -> c15(MARK(adx(tl(tl(nats))))) MARK(incr(adx(tl(tl(adx(y0)))))) -> c15(MARK(adx(tl(tl(adx(y0)))))) MARK(incr(adx(tl(tl(incr(y0)))))) -> c15(MARK(adx(tl(tl(incr(y0)))))) MARK(incr(adx(tl(tl(hd(y0)))))) -> c15(MARK(adx(tl(tl(hd(y0)))))) MARK(incr(adx(tl(tl(tl(y0)))))) -> c15(MARK(adx(tl(tl(tl(y0)))))) MARK(incr(adx(tl(tl(cons(y0, y1)))))) -> c15(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(incr(adx(tl(tl(y0))))) -> c15(MARK(adx(tl(tl(y0))))) MARK(incr(adx(tl(nats)))) -> c15(MARK(adx(tl(nats)))) MARK(incr(adx(hd(adx(0))))) -> c15(MARK(adx(hd(adx(0))))) MARK(incr(adx(hd(adx(s(y0)))))) -> c15(MARK(adx(hd(adx(s(y0)))))) MARK(incr(adx(hd(incr(0))))) -> c15(MARK(adx(hd(incr(0))))) MARK(incr(adx(hd(incr(s(y0)))))) -> c15(MARK(adx(hd(incr(s(y0)))))) MARK(incr(adx(hd(hd(zeros))))) -> c15(MARK(adx(hd(hd(zeros))))) MARK(incr(adx(tl(hd(zeros))))) -> c15(MARK(adx(tl(hd(zeros))))) MARK(incr(adx(tl(adx(0))))) -> c15(MARK(adx(tl(adx(0))))) MARK(incr(adx(hd(tl(zeros))))) -> c15(MARK(adx(hd(tl(zeros))))) MARK(incr(adx(tl(tl(zeros))))) -> c15(MARK(adx(tl(tl(zeros))))) MARK(incr(adx(tl(adx(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) MARK(incr(adx(tl(incr(0))))) -> c15(MARK(adx(tl(incr(0))))) MARK(incr(hd(adx(nats)))) -> c15(MARK(hd(adx(nats)))) MARK(incr(hd(adx(zeros)))) -> c15(MARK(hd(adx(zeros)))) MARK(incr(hd(adx(cons(y0, y1))))) -> c15(MARK(hd(adx(cons(y0, y1))))) MARK(incr(tl(adx(nats)))) -> c15(MARK(tl(adx(nats)))) MARK(incr(tl(adx(zeros)))) -> c15(MARK(tl(adx(zeros)))) MARK(incr(tl(adx(cons(y0, y1))))) -> c15(MARK(tl(adx(cons(y0, y1))))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) MARK(hd(incr(nats))) -> c16(A__HD(a__incr(a__nats))) MARK(hd(incr(zeros))) -> c16(A__HD(a__incr(a__zeros))) MARK(tl(incr(nats))) -> c17(A__TL(a__incr(a__nats))) MARK(tl(incr(zeros))) -> c17(A__TL(a__incr(a__zeros))) MARK(tl(incr(cons(z0, z1)))) -> c17(A__TL(a__incr(cons(z0, z1)))) MARK(hd(cons(adx(y0), z1))) -> c16(A__HD(cons(adx(y0), z1))) MARK(hd(cons(incr(y0), z1))) -> c16(A__HD(cons(incr(y0), z1))) MARK(hd(cons(hd(cons(y0, y1)), z1))) -> c16(A__HD(cons(hd(cons(y0, y1)), z1))) MARK(hd(cons(tl(cons(y0, y1)), z1))) -> c16(A__HD(cons(tl(cons(y0, y1)), z1))) MARK(hd(cons(hd(adx(nats)), z1))) -> c16(A__HD(cons(hd(adx(nats)), z1))) MARK(hd(cons(hd(adx(adx(y0))), z1))) -> c16(A__HD(cons(hd(adx(adx(y0))), z1))) MARK(hd(cons(hd(adx(zeros)), z1))) -> c16(A__HD(cons(hd(adx(zeros)), z1))) MARK(hd(cons(hd(adx(incr(y0))), z1))) -> c16(A__HD(cons(hd(adx(incr(y0))), z1))) MARK(hd(cons(hd(adx(hd(y0))), z1))) -> c16(A__HD(cons(hd(adx(hd(y0))), z1))) MARK(hd(cons(hd(adx(tl(y0))), z1))) -> c16(A__HD(cons(hd(adx(tl(y0))), z1))) MARK(hd(cons(hd(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(adx(cons(y0, y1))), z1))) MARK(hd(cons(hd(adx(y0)), z1))) -> c16(A__HD(cons(hd(adx(y0)), z1))) MARK(hd(cons(hd(incr(nats)), z1))) -> c16(A__HD(cons(hd(incr(nats)), z1))) MARK(hd(cons(hd(incr(adx(y0))), z1))) -> c16(A__HD(cons(hd(incr(adx(y0))), z1))) MARK(hd(cons(hd(incr(zeros)), z1))) -> c16(A__HD(cons(hd(incr(zeros)), z1))) MARK(hd(cons(hd(incr(incr(y0))), z1))) -> c16(A__HD(cons(hd(incr(incr(y0))), z1))) MARK(hd(cons(hd(incr(hd(y0))), z1))) -> c16(A__HD(cons(hd(incr(hd(y0))), z1))) MARK(hd(cons(hd(incr(tl(y0))), z1))) -> c16(A__HD(cons(hd(incr(tl(y0))), z1))) MARK(hd(cons(hd(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(incr(cons(y0, y1))), z1))) MARK(hd(cons(hd(incr(y0)), z1))) -> c16(A__HD(cons(hd(incr(y0)), z1))) MARK(hd(cons(hd(hd(nats)), z1))) -> c16(A__HD(cons(hd(hd(nats)), z1))) MARK(hd(cons(hd(hd(adx(y0))), z1))) -> c16(A__HD(cons(hd(hd(adx(y0))), z1))) MARK(hd(cons(hd(hd(zeros)), z1))) -> c16(A__HD(cons(hd(hd(zeros)), z1))) MARK(hd(cons(hd(hd(incr(y0))), z1))) -> c16(A__HD(cons(hd(hd(incr(y0))), z1))) MARK(hd(cons(hd(hd(hd(y0))), z1))) -> c16(A__HD(cons(hd(hd(hd(y0))), z1))) MARK(hd(cons(hd(hd(tl(y0))), z1))) -> c16(A__HD(cons(hd(hd(tl(y0))), z1))) MARK(hd(cons(hd(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(hd(cons(y0, y1))), z1))) MARK(hd(cons(hd(hd(y0)), z1))) -> c16(A__HD(cons(hd(hd(y0)), z1))) MARK(hd(cons(hd(tl(nats)), z1))) -> c16(A__HD(cons(hd(tl(nats)), z1))) MARK(hd(cons(hd(tl(adx(y0))), z1))) -> c16(A__HD(cons(hd(tl(adx(y0))), z1))) MARK(hd(cons(hd(tl(zeros)), z1))) -> c16(A__HD(cons(hd(tl(zeros)), z1))) MARK(hd(cons(hd(tl(incr(y0))), z1))) -> c16(A__HD(cons(hd(tl(incr(y0))), z1))) MARK(hd(cons(hd(tl(hd(y0))), z1))) -> c16(A__HD(cons(hd(tl(hd(y0))), z1))) MARK(hd(cons(hd(tl(tl(y0))), z1))) -> c16(A__HD(cons(hd(tl(tl(y0))), z1))) MARK(hd(cons(hd(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(hd(tl(cons(y0, y1))), z1))) MARK(hd(cons(hd(tl(y0)), z1))) -> c16(A__HD(cons(hd(tl(y0)), z1))) MARK(hd(cons(hd(nats), z1))) -> c16(A__HD(cons(hd(nats), z1))) MARK(hd(cons(tl(adx(nats)), z1))) -> c16(A__HD(cons(tl(adx(nats)), z1))) MARK(hd(cons(tl(adx(adx(y0))), z1))) -> c16(A__HD(cons(tl(adx(adx(y0))), z1))) MARK(hd(cons(tl(adx(zeros)), z1))) -> c16(A__HD(cons(tl(adx(zeros)), z1))) MARK(hd(cons(tl(adx(incr(y0))), z1))) -> c16(A__HD(cons(tl(adx(incr(y0))), z1))) MARK(hd(cons(tl(adx(hd(y0))), z1))) -> c16(A__HD(cons(tl(adx(hd(y0))), z1))) MARK(hd(cons(tl(adx(tl(y0))), z1))) -> c16(A__HD(cons(tl(adx(tl(y0))), z1))) MARK(hd(cons(tl(adx(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(adx(cons(y0, y1))), z1))) MARK(hd(cons(tl(adx(0)), z1))) -> c16(A__HD(cons(tl(adx(0)), z1))) MARK(hd(cons(tl(adx(s(y0))), z1))) -> c16(A__HD(cons(tl(adx(s(y0))), z1))) MARK(hd(cons(tl(adx(y0)), z1))) -> c16(A__HD(cons(tl(adx(y0)), z1))) MARK(hd(cons(tl(incr(nats)), z1))) -> c16(A__HD(cons(tl(incr(nats)), z1))) MARK(hd(cons(tl(incr(adx(y0))), z1))) -> c16(A__HD(cons(tl(incr(adx(y0))), z1))) MARK(hd(cons(tl(incr(zeros)), z1))) -> c16(A__HD(cons(tl(incr(zeros)), z1))) MARK(hd(cons(tl(incr(incr(y0))), z1))) -> c16(A__HD(cons(tl(incr(incr(y0))), z1))) MARK(hd(cons(tl(incr(hd(y0))), z1))) -> c16(A__HD(cons(tl(incr(hd(y0))), z1))) MARK(hd(cons(tl(incr(tl(y0))), z1))) -> c16(A__HD(cons(tl(incr(tl(y0))), z1))) MARK(hd(cons(tl(incr(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(incr(cons(y0, y1))), z1))) MARK(hd(cons(tl(incr(0)), z1))) -> c16(A__HD(cons(tl(incr(0)), z1))) MARK(hd(cons(tl(incr(s(y0))), z1))) -> c16(A__HD(cons(tl(incr(s(y0))), z1))) MARK(hd(cons(tl(incr(y0)), z1))) -> c16(A__HD(cons(tl(incr(y0)), z1))) MARK(hd(cons(tl(hd(nats)), z1))) -> c16(A__HD(cons(tl(hd(nats)), z1))) MARK(hd(cons(tl(hd(adx(y0))), z1))) -> c16(A__HD(cons(tl(hd(adx(y0))), z1))) MARK(hd(cons(tl(hd(zeros)), z1))) -> c16(A__HD(cons(tl(hd(zeros)), z1))) MARK(hd(cons(tl(hd(incr(y0))), z1))) -> c16(A__HD(cons(tl(hd(incr(y0))), z1))) MARK(hd(cons(tl(hd(hd(y0))), z1))) -> c16(A__HD(cons(tl(hd(hd(y0))), z1))) MARK(hd(cons(tl(hd(tl(y0))), z1))) -> c16(A__HD(cons(tl(hd(tl(y0))), z1))) MARK(hd(cons(tl(hd(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(hd(cons(y0, y1))), z1))) MARK(hd(cons(tl(hd(y0)), z1))) -> c16(A__HD(cons(tl(hd(y0)), z1))) MARK(hd(cons(tl(tl(nats)), z1))) -> c16(A__HD(cons(tl(tl(nats)), z1))) MARK(hd(cons(tl(tl(adx(y0))), z1))) -> c16(A__HD(cons(tl(tl(adx(y0))), z1))) MARK(hd(cons(tl(tl(zeros)), z1))) -> c16(A__HD(cons(tl(tl(zeros)), z1))) MARK(hd(cons(tl(tl(incr(y0))), z1))) -> c16(A__HD(cons(tl(tl(incr(y0))), z1))) MARK(hd(cons(tl(tl(hd(y0))), z1))) -> c16(A__HD(cons(tl(tl(hd(y0))), z1))) MARK(hd(cons(tl(tl(tl(y0))), z1))) -> c16(A__HD(cons(tl(tl(tl(y0))), z1))) MARK(hd(cons(tl(tl(cons(y0, y1))), z1))) -> c16(A__HD(cons(tl(tl(cons(y0, y1))), z1))) MARK(hd(cons(tl(tl(y0)), z1))) -> c16(A__HD(cons(tl(tl(y0)), z1))) MARK(hd(cons(tl(nats), z1))) -> c16(A__HD(cons(tl(nats), z1))) MARK(hd(cons(hd(adx(0)), z1))) -> c16(A__HD(cons(hd(adx(0)), z1))) MARK(hd(cons(hd(adx(s(y0))), z1))) -> c16(A__HD(cons(hd(adx(s(y0))), z1))) MARK(hd(cons(hd(incr(0)), z1))) -> c16(A__HD(cons(hd(incr(0)), z1))) MARK(hd(cons(hd(incr(s(y0))), z1))) -> c16(A__HD(cons(hd(incr(s(y0))), z1))) MARK(tl(cons(z0, adx(y1)))) -> c17(A__TL(cons(z0, adx(y1)))) MARK(tl(cons(z0, incr(y1)))) -> c17(A__TL(cons(z0, incr(y1)))) MARK(tl(cons(z0, hd(cons(y1, y2))))) -> c17(A__TL(cons(z0, hd(cons(y1, y2))))) MARK(tl(cons(z0, tl(cons(y1, y2))))) -> c17(A__TL(cons(z0, tl(cons(y1, y2))))) MARK(tl(cons(z0, hd(adx(nats))))) -> c17(A__TL(cons(z0, hd(adx(nats))))) MARK(tl(cons(z0, hd(adx(adx(y1)))))) -> c17(A__TL(cons(z0, hd(adx(adx(y1)))))) MARK(tl(cons(z0, hd(adx(zeros))))) -> c17(A__TL(cons(z0, hd(adx(zeros))))) MARK(tl(cons(z0, hd(adx(incr(y1)))))) -> c17(A__TL(cons(z0, hd(adx(incr(y1)))))) MARK(tl(cons(z0, hd(adx(hd(y1)))))) -> c17(A__TL(cons(z0, hd(adx(hd(y1)))))) MARK(tl(cons(z0, hd(adx(tl(y1)))))) -> c17(A__TL(cons(z0, hd(adx(tl(y1)))))) MARK(tl(cons(z0, hd(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(adx(cons(y1, y2)))))) MARK(tl(cons(z0, hd(adx(y1))))) -> c17(A__TL(cons(z0, hd(adx(y1))))) MARK(tl(cons(z0, hd(incr(nats))))) -> c17(A__TL(cons(z0, hd(incr(nats))))) MARK(tl(cons(z0, hd(incr(adx(y1)))))) -> c17(A__TL(cons(z0, hd(incr(adx(y1)))))) MARK(tl(cons(z0, hd(incr(zeros))))) -> c17(A__TL(cons(z0, hd(incr(zeros))))) MARK(tl(cons(z0, hd(incr(incr(y1)))))) -> c17(A__TL(cons(z0, hd(incr(incr(y1)))))) MARK(tl(cons(z0, hd(incr(hd(y1)))))) -> c17(A__TL(cons(z0, hd(incr(hd(y1)))))) MARK(tl(cons(z0, hd(incr(tl(y1)))))) -> c17(A__TL(cons(z0, hd(incr(tl(y1)))))) MARK(tl(cons(z0, hd(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(incr(cons(y1, y2)))))) MARK(tl(cons(z0, hd(incr(y1))))) -> c17(A__TL(cons(z0, hd(incr(y1))))) MARK(tl(cons(z0, hd(hd(nats))))) -> c17(A__TL(cons(z0, hd(hd(nats))))) MARK(tl(cons(z0, hd(hd(adx(y1)))))) -> c17(A__TL(cons(z0, hd(hd(adx(y1)))))) MARK(tl(cons(z0, hd(hd(incr(y1)))))) -> c17(A__TL(cons(z0, hd(hd(incr(y1)))))) MARK(tl(cons(z0, hd(hd(hd(y1)))))) -> c17(A__TL(cons(z0, hd(hd(hd(y1)))))) MARK(tl(cons(z0, hd(hd(tl(y1)))))) -> c17(A__TL(cons(z0, hd(hd(tl(y1)))))) MARK(tl(cons(z0, hd(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(hd(cons(y1, y2)))))) MARK(tl(cons(z0, hd(hd(y1))))) -> c17(A__TL(cons(z0, hd(hd(y1))))) MARK(tl(cons(z0, hd(tl(nats))))) -> c17(A__TL(cons(z0, hd(tl(nats))))) MARK(tl(cons(z0, hd(tl(adx(y1)))))) -> c17(A__TL(cons(z0, hd(tl(adx(y1)))))) MARK(tl(cons(z0, hd(tl(zeros))))) -> c17(A__TL(cons(z0, hd(tl(zeros))))) MARK(tl(cons(z0, hd(tl(incr(y1)))))) -> c17(A__TL(cons(z0, hd(tl(incr(y1)))))) MARK(tl(cons(z0, hd(tl(hd(y1)))))) -> c17(A__TL(cons(z0, hd(tl(hd(y1)))))) MARK(tl(cons(z0, hd(tl(tl(y1)))))) -> c17(A__TL(cons(z0, hd(tl(tl(y1)))))) MARK(tl(cons(z0, hd(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, hd(tl(cons(y1, y2)))))) MARK(tl(cons(z0, hd(tl(y1))))) -> c17(A__TL(cons(z0, hd(tl(y1))))) MARK(tl(cons(z0, hd(nats)))) -> c17(A__TL(cons(z0, hd(nats)))) MARK(tl(cons(z0, tl(adx(nats))))) -> c17(A__TL(cons(z0, tl(adx(nats))))) MARK(tl(cons(z0, tl(adx(adx(y1)))))) -> c17(A__TL(cons(z0, tl(adx(adx(y1)))))) MARK(tl(cons(z0, tl(adx(zeros))))) -> c17(A__TL(cons(z0, tl(adx(zeros))))) MARK(tl(cons(z0, tl(adx(incr(y1)))))) -> c17(A__TL(cons(z0, tl(adx(incr(y1)))))) MARK(tl(cons(z0, tl(adx(hd(y1)))))) -> c17(A__TL(cons(z0, tl(adx(hd(y1)))))) MARK(tl(cons(z0, tl(adx(tl(y1)))))) -> c17(A__TL(cons(z0, tl(adx(tl(y1)))))) MARK(tl(cons(z0, tl(adx(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(adx(cons(y1, y2)))))) MARK(tl(cons(z0, tl(adx(s(y1)))))) -> c17(A__TL(cons(z0, tl(adx(s(y1)))))) MARK(tl(cons(z0, tl(adx(y1))))) -> c17(A__TL(cons(z0, tl(adx(y1))))) MARK(tl(cons(z0, tl(incr(nats))))) -> c17(A__TL(cons(z0, tl(incr(nats))))) MARK(tl(cons(z0, tl(incr(adx(y1)))))) -> c17(A__TL(cons(z0, tl(incr(adx(y1)))))) MARK(tl(cons(z0, tl(incr(zeros))))) -> c17(A__TL(cons(z0, tl(incr(zeros))))) MARK(tl(cons(z0, tl(incr(incr(y1)))))) -> c17(A__TL(cons(z0, tl(incr(incr(y1)))))) MARK(tl(cons(z0, tl(incr(hd(y1)))))) -> c17(A__TL(cons(z0, tl(incr(hd(y1)))))) MARK(tl(cons(z0, tl(incr(tl(y1)))))) -> c17(A__TL(cons(z0, tl(incr(tl(y1)))))) MARK(tl(cons(z0, tl(incr(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(incr(cons(y1, y2)))))) MARK(tl(cons(z0, tl(incr(0))))) -> c17(A__TL(cons(z0, tl(incr(0))))) MARK(tl(cons(z0, tl(incr(s(y1)))))) -> c17(A__TL(cons(z0, tl(incr(s(y1)))))) MARK(tl(cons(z0, tl(incr(y1))))) -> c17(A__TL(cons(z0, tl(incr(y1))))) MARK(tl(cons(z0, tl(hd(nats))))) -> c17(A__TL(cons(z0, tl(hd(nats))))) MARK(tl(cons(z0, tl(hd(adx(y1)))))) -> c17(A__TL(cons(z0, tl(hd(adx(y1)))))) MARK(tl(cons(z0, tl(hd(incr(y1)))))) -> c17(A__TL(cons(z0, tl(hd(incr(y1)))))) MARK(tl(cons(z0, tl(hd(hd(y1)))))) -> c17(A__TL(cons(z0, tl(hd(hd(y1)))))) MARK(tl(cons(z0, tl(hd(tl(y1)))))) -> c17(A__TL(cons(z0, tl(hd(tl(y1)))))) MARK(tl(cons(z0, tl(hd(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(hd(cons(y1, y2)))))) MARK(tl(cons(z0, tl(hd(y1))))) -> c17(A__TL(cons(z0, tl(hd(y1))))) MARK(tl(cons(z0, tl(tl(nats))))) -> c17(A__TL(cons(z0, tl(tl(nats))))) MARK(tl(cons(z0, tl(tl(adx(y1)))))) -> c17(A__TL(cons(z0, tl(tl(adx(y1)))))) MARK(tl(cons(z0, tl(tl(zeros))))) -> c17(A__TL(cons(z0, tl(tl(zeros))))) MARK(tl(cons(z0, tl(tl(incr(y1)))))) -> c17(A__TL(cons(z0, tl(tl(incr(y1)))))) MARK(tl(cons(z0, tl(tl(hd(y1)))))) -> c17(A__TL(cons(z0, tl(tl(hd(y1)))))) MARK(tl(cons(z0, tl(tl(tl(y1)))))) -> c17(A__TL(cons(z0, tl(tl(tl(y1)))))) MARK(tl(cons(z0, tl(tl(cons(y1, y2)))))) -> c17(A__TL(cons(z0, tl(tl(cons(y1, y2)))))) MARK(tl(cons(z0, tl(tl(y1))))) -> c17(A__TL(cons(z0, tl(tl(y1))))) MARK(tl(cons(z0, tl(nats)))) -> c17(A__TL(cons(z0, tl(nats)))) MARK(tl(cons(z0, hd(adx(0))))) -> c17(A__TL(cons(z0, hd(adx(0))))) MARK(tl(cons(z0, hd(adx(s(y1)))))) -> c17(A__TL(cons(z0, hd(adx(s(y1)))))) MARK(tl(cons(z0, hd(incr(0))))) -> c17(A__TL(cons(z0, hd(incr(0))))) MARK(tl(cons(z0, hd(incr(s(y1)))))) -> c17(A__TL(cons(z0, hd(incr(s(y1)))))) MARK(tl(cons(z0, hd(hd(zeros))))) -> c17(A__TL(cons(z0, hd(hd(zeros))))) MARK(tl(cons(z0, tl(hd(zeros))))) -> c17(A__TL(cons(z0, tl(hd(zeros))))) MARK(tl(cons(z0, tl(adx(0))))) -> c17(A__TL(cons(z0, tl(adx(0))))) MARK(hd(adx(adx(y0)))) -> c16(MARK(adx(adx(y0)))) MARK(hd(adx(incr(y0)))) -> c16(MARK(adx(incr(y0)))) MARK(hd(adx(hd(cons(y0, y1))))) -> c16(MARK(adx(hd(cons(y0, y1))))) MARK(hd(adx(tl(cons(y0, y1))))) -> c16(MARK(adx(tl(cons(y0, y1))))) MARK(hd(adx(hd(adx(nats))))) -> c16(MARK(adx(hd(adx(nats))))) MARK(hd(adx(hd(adx(adx(y0)))))) -> c16(MARK(adx(hd(adx(adx(y0)))))) MARK(hd(adx(hd(adx(zeros))))) -> c16(MARK(adx(hd(adx(zeros))))) MARK(hd(adx(hd(adx(incr(y0)))))) -> c16(MARK(adx(hd(adx(incr(y0)))))) MARK(hd(adx(hd(adx(hd(y0)))))) -> c16(MARK(adx(hd(adx(hd(y0)))))) MARK(hd(adx(hd(adx(tl(y0)))))) -> c16(MARK(adx(hd(adx(tl(y0)))))) MARK(hd(adx(hd(adx(cons(y0, y1)))))) -> c16(MARK(adx(hd(adx(cons(y0, y1)))))) MARK(hd(adx(hd(adx(y0))))) -> c16(MARK(adx(hd(adx(y0))))) MARK(hd(adx(hd(incr(nats))))) -> c16(MARK(adx(hd(incr(nats))))) MARK(hd(adx(hd(incr(adx(y0)))))) -> c16(MARK(adx(hd(incr(adx(y0)))))) MARK(hd(adx(hd(incr(zeros))))) -> c16(MARK(adx(hd(incr(zeros))))) MARK(hd(adx(hd(incr(incr(y0)))))) -> c16(MARK(adx(hd(incr(incr(y0)))))) MARK(hd(adx(hd(incr(hd(y0)))))) -> c16(MARK(adx(hd(incr(hd(y0)))))) MARK(hd(adx(hd(incr(tl(y0)))))) -> c16(MARK(adx(hd(incr(tl(y0)))))) MARK(hd(adx(hd(incr(cons(y0, y1)))))) -> c16(MARK(adx(hd(incr(cons(y0, y1)))))) MARK(hd(adx(hd(incr(y0))))) -> c16(MARK(adx(hd(incr(y0))))) MARK(hd(adx(hd(hd(nats))))) -> c16(MARK(adx(hd(hd(nats))))) MARK(hd(adx(hd(hd(adx(y0)))))) -> c16(MARK(adx(hd(hd(adx(y0)))))) MARK(hd(adx(hd(hd(incr(y0)))))) -> c16(MARK(adx(hd(hd(incr(y0)))))) MARK(hd(adx(hd(hd(hd(y0)))))) -> c16(MARK(adx(hd(hd(hd(y0)))))) MARK(hd(adx(hd(hd(tl(y0)))))) -> c16(MARK(adx(hd(hd(tl(y0)))))) MARK(hd(adx(hd(hd(cons(y0, y1)))))) -> c16(MARK(adx(hd(hd(cons(y0, y1)))))) MARK(hd(adx(hd(hd(y0))))) -> c16(MARK(adx(hd(hd(y0))))) MARK(hd(adx(hd(tl(nats))))) -> c16(MARK(adx(hd(tl(nats))))) MARK(hd(adx(hd(tl(adx(y0)))))) -> c16(MARK(adx(hd(tl(adx(y0)))))) MARK(hd(adx(hd(tl(incr(y0)))))) -> c16(MARK(adx(hd(tl(incr(y0)))))) MARK(hd(adx(hd(tl(hd(y0)))))) -> c16(MARK(adx(hd(tl(hd(y0)))))) MARK(hd(adx(hd(tl(tl(y0)))))) -> c16(MARK(adx(hd(tl(tl(y0)))))) MARK(hd(adx(hd(tl(cons(y0, y1)))))) -> c16(MARK(adx(hd(tl(cons(y0, y1)))))) MARK(hd(adx(hd(tl(y0))))) -> c16(MARK(adx(hd(tl(y0))))) MARK(hd(adx(hd(nats)))) -> c16(MARK(adx(hd(nats)))) MARK(hd(adx(tl(adx(nats))))) -> c16(MARK(adx(tl(adx(nats))))) MARK(hd(adx(tl(adx(adx(y0)))))) -> c16(MARK(adx(tl(adx(adx(y0)))))) MARK(hd(adx(tl(adx(zeros))))) -> c16(MARK(adx(tl(adx(zeros))))) MARK(hd(adx(tl(adx(incr(y0)))))) -> c16(MARK(adx(tl(adx(incr(y0)))))) MARK(hd(adx(tl(adx(hd(y0)))))) -> c16(MARK(adx(tl(adx(hd(y0)))))) MARK(hd(adx(tl(adx(tl(y0)))))) -> c16(MARK(adx(tl(adx(tl(y0)))))) MARK(hd(adx(tl(adx(cons(y0, y1)))))) -> c16(MARK(adx(tl(adx(cons(y0, y1)))))) MARK(hd(adx(tl(adx(y0))))) -> c16(MARK(adx(tl(adx(y0))))) MARK(hd(adx(tl(incr(nats))))) -> c16(MARK(adx(tl(incr(nats))))) MARK(hd(adx(tl(incr(adx(y0)))))) -> c16(MARK(adx(tl(incr(adx(y0)))))) MARK(hd(adx(tl(incr(zeros))))) -> c16(MARK(adx(tl(incr(zeros))))) MARK(hd(adx(tl(incr(incr(y0)))))) -> c16(MARK(adx(tl(incr(incr(y0)))))) MARK(hd(adx(tl(incr(hd(y0)))))) -> c16(MARK(adx(tl(incr(hd(y0)))))) MARK(hd(adx(tl(incr(tl(y0)))))) -> c16(MARK(adx(tl(incr(tl(y0)))))) MARK(hd(adx(tl(incr(cons(y0, y1)))))) -> c16(MARK(adx(tl(incr(cons(y0, y1)))))) MARK(hd(adx(tl(incr(s(y0)))))) -> c16(MARK(adx(tl(incr(s(y0)))))) MARK(hd(adx(tl(incr(y0))))) -> c16(MARK(adx(tl(incr(y0))))) MARK(hd(adx(tl(hd(nats))))) -> c16(MARK(adx(tl(hd(nats))))) MARK(hd(adx(tl(hd(adx(y0)))))) -> c16(MARK(adx(tl(hd(adx(y0)))))) MARK(hd(adx(tl(hd(incr(y0)))))) -> c16(MARK(adx(tl(hd(incr(y0)))))) MARK(hd(adx(tl(hd(hd(y0)))))) -> c16(MARK(adx(tl(hd(hd(y0)))))) MARK(hd(adx(tl(hd(tl(y0)))))) -> c16(MARK(adx(tl(hd(tl(y0)))))) MARK(hd(adx(tl(hd(cons(y0, y1)))))) -> c16(MARK(adx(tl(hd(cons(y0, y1)))))) MARK(hd(adx(tl(hd(y0))))) -> c16(MARK(adx(tl(hd(y0))))) MARK(hd(adx(tl(tl(nats))))) -> c16(MARK(adx(tl(tl(nats))))) MARK(hd(adx(tl(tl(adx(y0)))))) -> c16(MARK(adx(tl(tl(adx(y0)))))) MARK(hd(adx(tl(tl(incr(y0)))))) -> c16(MARK(adx(tl(tl(incr(y0)))))) MARK(hd(adx(tl(tl(hd(y0)))))) -> c16(MARK(adx(tl(tl(hd(y0)))))) MARK(hd(adx(tl(tl(tl(y0)))))) -> c16(MARK(adx(tl(tl(tl(y0)))))) MARK(hd(adx(tl(tl(cons(y0, y1)))))) -> c16(MARK(adx(tl(tl(cons(y0, y1)))))) MARK(hd(adx(tl(tl(y0))))) -> c16(MARK(adx(tl(tl(y0))))) MARK(hd(adx(tl(nats)))) -> c16(MARK(adx(tl(nats)))) MARK(hd(adx(hd(adx(0))))) -> c16(MARK(adx(hd(adx(0))))) MARK(hd(adx(hd(adx(s(y0)))))) -> c16(MARK(adx(hd(adx(s(y0)))))) MARK(hd(adx(hd(incr(0))))) -> c16(MARK(adx(hd(incr(0))))) MARK(hd(adx(hd(incr(s(y0)))))) -> c16(MARK(adx(hd(incr(s(y0)))))) MARK(hd(adx(hd(hd(zeros))))) -> c16(MARK(adx(hd(hd(zeros))))) MARK(hd(adx(tl(hd(zeros))))) -> c16(MARK(adx(tl(hd(zeros))))) MARK(hd(adx(tl(adx(0))))) -> c16(MARK(adx(tl(adx(0))))) MARK(hd(adx(hd(tl(zeros))))) -> c16(MARK(adx(hd(tl(zeros))))) MARK(hd(adx(tl(tl(zeros))))) -> c16(MARK(adx(tl(tl(zeros))))) MARK(hd(adx(tl(adx(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) MARK(hd(adx(tl(incr(0))))) -> c16(MARK(adx(tl(incr(0))))) MARK(hd(incr(incr(y0)))) -> c16(MARK(incr(incr(y0)))) MARK(hd(incr(hd(cons(y0, y1))))) -> c16(MARK(incr(hd(cons(y0, y1))))) MARK(hd(incr(tl(cons(y0, y1))))) -> c16(MARK(incr(tl(cons(y0, y1))))) MARK(hd(incr(hd(adx(adx(y0)))))) -> c16(MARK(incr(hd(adx(adx(y0)))))) MARK(hd(incr(hd(adx(incr(y0)))))) -> c16(MARK(incr(hd(adx(incr(y0)))))) MARK(hd(incr(hd(adx(hd(y0)))))) -> c16(MARK(incr(hd(adx(hd(y0)))))) MARK(hd(incr(hd(adx(tl(y0)))))) -> c16(MARK(incr(hd(adx(tl(y0)))))) MARK(hd(incr(hd(adx(y0))))) -> c16(MARK(incr(hd(adx(y0))))) MARK(hd(incr(hd(incr(nats))))) -> c16(MARK(incr(hd(incr(nats))))) MARK(hd(incr(hd(incr(adx(y0)))))) -> c16(MARK(incr(hd(incr(adx(y0)))))) MARK(hd(incr(hd(incr(zeros))))) -> c16(MARK(incr(hd(incr(zeros))))) MARK(hd(incr(hd(incr(incr(y0)))))) -> c16(MARK(incr(hd(incr(incr(y0)))))) MARK(hd(incr(hd(incr(hd(y0)))))) -> c16(MARK(incr(hd(incr(hd(y0)))))) MARK(hd(incr(hd(incr(tl(y0)))))) -> c16(MARK(incr(hd(incr(tl(y0)))))) MARK(hd(incr(hd(incr(cons(y0, y1)))))) -> c16(MARK(incr(hd(incr(cons(y0, y1)))))) MARK(hd(incr(hd(incr(y0))))) -> c16(MARK(incr(hd(incr(y0))))) MARK(hd(incr(hd(hd(nats))))) -> c16(MARK(incr(hd(hd(nats))))) MARK(hd(incr(hd(hd(adx(y0)))))) -> c16(MARK(incr(hd(hd(adx(y0)))))) MARK(hd(incr(hd(hd(incr(y0)))))) -> c16(MARK(incr(hd(hd(incr(y0)))))) MARK(hd(incr(hd(hd(hd(y0)))))) -> c16(MARK(incr(hd(hd(hd(y0)))))) MARK(hd(incr(hd(hd(tl(y0)))))) -> c16(MARK(incr(hd(hd(tl(y0)))))) MARK(hd(incr(hd(hd(cons(y0, y1)))))) -> c16(MARK(incr(hd(hd(cons(y0, y1)))))) MARK(hd(incr(hd(hd(y0))))) -> c16(MARK(incr(hd(hd(y0))))) MARK(hd(incr(hd(tl(nats))))) -> c16(MARK(incr(hd(tl(nats))))) MARK(hd(incr(hd(tl(adx(y0)))))) -> c16(MARK(incr(hd(tl(adx(y0)))))) MARK(hd(incr(hd(tl(incr(y0)))))) -> c16(MARK(incr(hd(tl(incr(y0)))))) MARK(hd(incr(hd(tl(hd(y0)))))) -> c16(MARK(incr(hd(tl(hd(y0)))))) MARK(hd(incr(hd(tl(tl(y0)))))) -> c16(MARK(incr(hd(tl(tl(y0)))))) MARK(hd(incr(hd(tl(cons(y0, y1)))))) -> c16(MARK(incr(hd(tl(cons(y0, y1)))))) MARK(hd(incr(hd(tl(y0))))) -> c16(MARK(incr(hd(tl(y0))))) MARK(hd(incr(hd(nats)))) -> c16(MARK(incr(hd(nats)))) MARK(hd(incr(tl(adx(adx(y0)))))) -> c16(MARK(incr(tl(adx(adx(y0)))))) MARK(hd(incr(tl(adx(incr(y0)))))) -> c16(MARK(incr(tl(adx(incr(y0)))))) MARK(hd(incr(tl(adx(hd(y0)))))) -> c16(MARK(incr(tl(adx(hd(y0)))))) MARK(hd(incr(tl(adx(tl(y0)))))) -> c16(MARK(incr(tl(adx(tl(y0)))))) MARK(hd(incr(tl(adx(y0))))) -> c16(MARK(incr(tl(adx(y0))))) MARK(hd(incr(tl(incr(nats))))) -> c16(MARK(incr(tl(incr(nats))))) MARK(hd(incr(tl(incr(adx(y0)))))) -> c16(MARK(incr(tl(incr(adx(y0)))))) MARK(hd(incr(tl(incr(zeros))))) -> c16(MARK(incr(tl(incr(zeros))))) MARK(hd(incr(tl(incr(incr(y0)))))) -> c16(MARK(incr(tl(incr(incr(y0)))))) MARK(hd(incr(tl(incr(hd(y0)))))) -> c16(MARK(incr(tl(incr(hd(y0)))))) MARK(hd(incr(tl(incr(tl(y0)))))) -> c16(MARK(incr(tl(incr(tl(y0)))))) MARK(hd(incr(tl(incr(cons(y0, y1)))))) -> c16(MARK(incr(tl(incr(cons(y0, y1)))))) MARK(hd(incr(tl(incr(y0))))) -> c16(MARK(incr(tl(incr(y0))))) MARK(hd(incr(tl(hd(nats))))) -> c16(MARK(incr(tl(hd(nats))))) MARK(hd(incr(tl(hd(adx(y0)))))) -> c16(MARK(incr(tl(hd(adx(y0)))))) MARK(hd(incr(tl(hd(incr(y0)))))) -> c16(MARK(incr(tl(hd(incr(y0)))))) MARK(hd(incr(tl(hd(hd(y0)))))) -> c16(MARK(incr(tl(hd(hd(y0)))))) MARK(hd(incr(tl(hd(tl(y0)))))) -> c16(MARK(incr(tl(hd(tl(y0)))))) MARK(hd(incr(tl(hd(cons(y0, y1)))))) -> c16(MARK(incr(tl(hd(cons(y0, y1)))))) MARK(hd(incr(tl(hd(y0))))) -> c16(MARK(incr(tl(hd(y0))))) MARK(hd(incr(tl(tl(nats))))) -> c16(MARK(incr(tl(tl(nats))))) MARK(hd(incr(tl(tl(adx(y0)))))) -> c16(MARK(incr(tl(tl(adx(y0)))))) MARK(hd(incr(tl(tl(incr(y0)))))) -> c16(MARK(incr(tl(tl(incr(y0)))))) MARK(hd(incr(tl(tl(hd(y0)))))) -> c16(MARK(incr(tl(tl(hd(y0)))))) MARK(hd(incr(tl(tl(tl(y0)))))) -> c16(MARK(incr(tl(tl(tl(y0)))))) MARK(hd(incr(tl(tl(cons(y0, y1)))))) -> c16(MARK(incr(tl(tl(cons(y0, y1)))))) MARK(hd(incr(tl(tl(y0))))) -> c16(MARK(incr(tl(tl(y0))))) MARK(hd(incr(tl(nats)))) -> c16(MARK(incr(tl(nats)))) MARK(hd(incr(hd(incr(0))))) -> c16(MARK(incr(hd(incr(0))))) MARK(hd(incr(hd(incr(s(y0)))))) -> c16(MARK(incr(hd(incr(s(y0)))))) MARK(hd(incr(hd(hd(zeros))))) -> c16(MARK(incr(hd(hd(zeros))))) MARK(hd(incr(tl(hd(zeros))))) -> c16(MARK(incr(tl(hd(zeros))))) MARK(hd(incr(hd(tl(zeros))))) -> c16(MARK(incr(hd(tl(zeros))))) MARK(hd(incr(tl(tl(zeros))))) -> c16(MARK(incr(tl(tl(zeros))))) MARK(hd(incr(tl(incr(0))))) -> c16(MARK(incr(tl(incr(0))))) MARK(hd(incr(adx(adx(y0))))) -> c16(MARK(incr(adx(adx(y0))))) MARK(hd(incr(adx(incr(y0))))) -> c16(MARK(incr(adx(incr(y0))))) MARK(hd(incr(adx(hd(cons(y0, y1)))))) -> c16(MARK(incr(adx(hd(cons(y0, y1)))))) MARK(hd(incr(adx(tl(cons(y0, y1)))))) -> c16(MARK(incr(adx(tl(cons(y0, y1)))))) MARK(hd(incr(adx(hd(adx(nats)))))) -> c16(MARK(incr(adx(hd(adx(nats)))))) MARK(hd(incr(adx(hd(adx(adx(y0))))))) -> c16(MARK(incr(adx(hd(adx(adx(y0))))))) MARK(hd(incr(adx(hd(adx(zeros)))))) -> c16(MARK(incr(adx(hd(adx(zeros)))))) MARK(hd(incr(adx(hd(adx(incr(y0))))))) -> c16(MARK(incr(adx(hd(adx(incr(y0))))))) MARK(hd(incr(adx(hd(adx(hd(y0))))))) -> c16(MARK(incr(adx(hd(adx(hd(y0))))))) MARK(hd(incr(adx(hd(adx(tl(y0))))))) -> c16(MARK(incr(adx(hd(adx(tl(y0))))))) MARK(hd(incr(adx(hd(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(adx(cons(y0, y1))))))) MARK(hd(incr(adx(hd(adx(y0)))))) -> c16(MARK(incr(adx(hd(adx(y0)))))) MARK(hd(incr(adx(hd(incr(nats)))))) -> c16(MARK(incr(adx(hd(incr(nats)))))) MARK(hd(incr(adx(hd(incr(adx(y0))))))) -> c16(MARK(incr(adx(hd(incr(adx(y0))))))) MARK(hd(incr(adx(hd(incr(zeros)))))) -> c16(MARK(incr(adx(hd(incr(zeros)))))) MARK(hd(incr(adx(hd(incr(incr(y0))))))) -> c16(MARK(incr(adx(hd(incr(incr(y0))))))) MARK(hd(incr(adx(hd(incr(hd(y0))))))) -> c16(MARK(incr(adx(hd(incr(hd(y0))))))) MARK(hd(incr(adx(hd(incr(tl(y0))))))) -> c16(MARK(incr(adx(hd(incr(tl(y0))))))) MARK(hd(incr(adx(hd(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(incr(cons(y0, y1))))))) MARK(hd(incr(adx(hd(incr(y0)))))) -> c16(MARK(incr(adx(hd(incr(y0)))))) MARK(hd(incr(adx(hd(hd(nats)))))) -> c16(MARK(incr(adx(hd(hd(nats)))))) MARK(hd(incr(adx(hd(hd(adx(y0))))))) -> c16(MARK(incr(adx(hd(hd(adx(y0))))))) MARK(hd(incr(adx(hd(hd(incr(y0))))))) -> c16(MARK(incr(adx(hd(hd(incr(y0))))))) MARK(hd(incr(adx(hd(hd(hd(y0))))))) -> c16(MARK(incr(adx(hd(hd(hd(y0))))))) MARK(hd(incr(adx(hd(hd(tl(y0))))))) -> c16(MARK(incr(adx(hd(hd(tl(y0))))))) MARK(hd(incr(adx(hd(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(hd(cons(y0, y1))))))) MARK(hd(incr(adx(hd(hd(y0)))))) -> c16(MARK(incr(adx(hd(hd(y0)))))) MARK(hd(incr(adx(hd(tl(nats)))))) -> c16(MARK(incr(adx(hd(tl(nats)))))) MARK(hd(incr(adx(hd(tl(adx(y0))))))) -> c16(MARK(incr(adx(hd(tl(adx(y0))))))) MARK(hd(incr(adx(hd(tl(incr(y0))))))) -> c16(MARK(incr(adx(hd(tl(incr(y0))))))) MARK(hd(incr(adx(hd(tl(hd(y0))))))) -> c16(MARK(incr(adx(hd(tl(hd(y0))))))) MARK(hd(incr(adx(hd(tl(tl(y0))))))) -> c16(MARK(incr(adx(hd(tl(tl(y0))))))) MARK(hd(incr(adx(hd(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(hd(tl(cons(y0, y1))))))) MARK(hd(incr(adx(hd(tl(y0)))))) -> c16(MARK(incr(adx(hd(tl(y0)))))) MARK(hd(incr(adx(hd(nats))))) -> c16(MARK(incr(adx(hd(nats))))) MARK(hd(incr(adx(tl(adx(nats)))))) -> c16(MARK(incr(adx(tl(adx(nats)))))) MARK(hd(incr(adx(tl(adx(adx(y0))))))) -> c16(MARK(incr(adx(tl(adx(adx(y0))))))) MARK(hd(incr(adx(tl(adx(zeros)))))) -> c16(MARK(incr(adx(tl(adx(zeros)))))) MARK(hd(incr(adx(tl(adx(incr(y0))))))) -> c16(MARK(incr(adx(tl(adx(incr(y0))))))) MARK(hd(incr(adx(tl(adx(hd(y0))))))) -> c16(MARK(incr(adx(tl(adx(hd(y0))))))) MARK(hd(incr(adx(tl(adx(tl(y0))))))) -> c16(MARK(incr(adx(tl(adx(tl(y0))))))) MARK(hd(incr(adx(tl(adx(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(adx(cons(y0, y1))))))) MARK(hd(incr(adx(tl(adx(y0)))))) -> c16(MARK(incr(adx(tl(adx(y0)))))) MARK(hd(incr(adx(tl(incr(nats)))))) -> c16(MARK(incr(adx(tl(incr(nats)))))) MARK(hd(incr(adx(tl(incr(adx(y0))))))) -> c16(MARK(incr(adx(tl(incr(adx(y0))))))) MARK(hd(incr(adx(tl(incr(zeros)))))) -> c16(MARK(incr(adx(tl(incr(zeros)))))) MARK(hd(incr(adx(tl(incr(incr(y0))))))) -> c16(MARK(incr(adx(tl(incr(incr(y0))))))) MARK(hd(incr(adx(tl(incr(hd(y0))))))) -> c16(MARK(incr(adx(tl(incr(hd(y0))))))) MARK(hd(incr(adx(tl(incr(tl(y0))))))) -> c16(MARK(incr(adx(tl(incr(tl(y0))))))) MARK(hd(incr(adx(tl(incr(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(incr(cons(y0, y1))))))) MARK(hd(incr(adx(tl(incr(s(y0))))))) -> c16(MARK(incr(adx(tl(incr(s(y0))))))) MARK(hd(incr(adx(tl(incr(y0)))))) -> c16(MARK(incr(adx(tl(incr(y0)))))) MARK(hd(incr(adx(tl(hd(nats)))))) -> c16(MARK(incr(adx(tl(hd(nats)))))) MARK(hd(incr(adx(tl(hd(adx(y0))))))) -> c16(MARK(incr(adx(tl(hd(adx(y0))))))) MARK(hd(incr(adx(tl(hd(incr(y0))))))) -> c16(MARK(incr(adx(tl(hd(incr(y0))))))) MARK(hd(incr(adx(tl(hd(hd(y0))))))) -> c16(MARK(incr(adx(tl(hd(hd(y0))))))) MARK(hd(incr(adx(tl(hd(tl(y0))))))) -> c16(MARK(incr(adx(tl(hd(tl(y0))))))) MARK(hd(incr(adx(tl(hd(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(hd(cons(y0, y1))))))) MARK(hd(incr(adx(tl(hd(y0)))))) -> c16(MARK(incr(adx(tl(hd(y0)))))) MARK(hd(incr(adx(tl(tl(nats)))))) -> c16(MARK(incr(adx(tl(tl(nats)))))) MARK(hd(incr(adx(tl(tl(adx(y0))))))) -> c16(MARK(incr(adx(tl(tl(adx(y0))))))) MARK(hd(incr(adx(tl(tl(incr(y0))))))) -> c16(MARK(incr(adx(tl(tl(incr(y0))))))) MARK(hd(incr(adx(tl(tl(hd(y0))))))) -> c16(MARK(incr(adx(tl(tl(hd(y0))))))) MARK(hd(incr(adx(tl(tl(tl(y0))))))) -> c16(MARK(incr(adx(tl(tl(tl(y0))))))) MARK(hd(incr(adx(tl(tl(cons(y0, y1))))))) -> c16(MARK(incr(adx(tl(tl(cons(y0, y1))))))) MARK(hd(incr(adx(tl(tl(y0)))))) -> c16(MARK(incr(adx(tl(tl(y0)))))) MARK(hd(incr(adx(tl(nats))))) -> c16(MARK(incr(adx(tl(nats))))) MARK(hd(incr(adx(hd(adx(0)))))) -> c16(MARK(incr(adx(hd(adx(0)))))) MARK(hd(incr(adx(hd(adx(s(y0))))))) -> c16(MARK(incr(adx(hd(adx(s(y0))))))) MARK(hd(incr(adx(hd(incr(0)))))) -> c16(MARK(incr(adx(hd(incr(0)))))) MARK(hd(incr(adx(hd(incr(s(y0))))))) -> c16(MARK(incr(adx(hd(incr(s(y0))))))) MARK(hd(incr(adx(hd(hd(zeros)))))) -> c16(MARK(incr(adx(hd(hd(zeros)))))) MARK(hd(incr(adx(tl(hd(zeros)))))) -> c16(MARK(incr(adx(tl(hd(zeros)))))) MARK(hd(incr(adx(tl(adx(0)))))) -> c16(MARK(incr(adx(tl(adx(0)))))) MARK(hd(incr(adx(hd(tl(zeros)))))) -> c16(MARK(incr(adx(hd(tl(zeros)))))) MARK(hd(incr(adx(tl(tl(zeros)))))) -> c16(MARK(incr(adx(tl(tl(zeros)))))) MARK(hd(incr(adx(tl(adx(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) MARK(hd(incr(adx(tl(incr(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) MARK(hd(incr(hd(adx(nats))))) -> c16(MARK(incr(hd(adx(nats))))) MARK(hd(incr(hd(adx(zeros))))) -> c16(MARK(incr(hd(adx(zeros))))) MARK(hd(incr(hd(adx(cons(y0, y1)))))) -> c16(MARK(incr(hd(adx(cons(y0, y1)))))) MARK(hd(incr(tl(adx(nats))))) -> c16(MARK(incr(tl(adx(nats))))) MARK(hd(incr(tl(adx(zeros))))) -> c16(MARK(incr(tl(adx(zeros))))) MARK(hd(incr(tl(adx(cons(y0, y1)))))) -> c16(MARK(incr(tl(adx(cons(y0, y1)))))) MARK(hd(incr(tl(incr(s(y0)))))) -> c16(MARK(incr(tl(incr(s(y0)))))) MARK(hd(hd(adx(adx(y0))))) -> c16(MARK(hd(adx(adx(y0))))) MARK(hd(hd(adx(incr(y0))))) -> c16(MARK(hd(adx(incr(y0))))) MARK(hd(hd(adx(hd(y0))))) -> c16(MARK(hd(adx(hd(y0))))) MARK(hd(hd(adx(tl(y0))))) -> c16(MARK(hd(adx(tl(y0))))) MARK(hd(hd(incr(adx(y0))))) -> c16(MARK(hd(incr(adx(y0))))) MARK(hd(hd(incr(incr(y0))))) -> c16(MARK(hd(incr(incr(y0))))) MARK(hd(hd(incr(hd(y0))))) -> c16(MARK(hd(incr(hd(y0))))) MARK(hd(hd(incr(tl(y0))))) -> c16(MARK(hd(incr(tl(y0))))) MARK(hd(hd(hd(nats)))) -> c16(MARK(hd(hd(nats)))) MARK(hd(hd(hd(adx(y0))))) -> c16(MARK(hd(hd(adx(y0))))) MARK(hd(hd(hd(incr(y0))))) -> c16(MARK(hd(hd(incr(y0))))) MARK(hd(hd(hd(hd(y0))))) -> c16(MARK(hd(hd(hd(y0))))) MARK(hd(hd(hd(tl(y0))))) -> c16(MARK(hd(hd(tl(y0))))) MARK(hd(hd(hd(cons(y0, y1))))) -> c16(MARK(hd(hd(cons(y0, y1))))) MARK(hd(hd(hd(y0)))) -> c16(MARK(hd(hd(y0)))) MARK(hd(hd(tl(nats)))) -> c16(MARK(hd(tl(nats)))) MARK(hd(hd(tl(adx(y0))))) -> c16(MARK(hd(tl(adx(y0))))) MARK(hd(hd(tl(incr(y0))))) -> c16(MARK(hd(tl(incr(y0))))) MARK(hd(hd(tl(hd(y0))))) -> c16(MARK(hd(tl(hd(y0))))) MARK(hd(hd(tl(tl(y0))))) -> c16(MARK(hd(tl(tl(y0))))) MARK(hd(hd(tl(cons(y0, y1))))) -> c16(MARK(hd(tl(cons(y0, y1))))) MARK(hd(hd(tl(y0)))) -> c16(MARK(hd(tl(y0)))) MARK(hd(hd(nats))) -> c16(MARK(hd(nats))) MARK(hd(hd(hd(zeros)))) -> c16(MARK(hd(hd(zeros)))) MARK(hd(hd(tl(zeros)))) -> c16(MARK(hd(tl(zeros)))) MARK(hd(hd(adx(nats)))) -> c16(MARK(hd(adx(nats)))) MARK(hd(hd(adx(zeros)))) -> c16(MARK(hd(adx(zeros)))) MARK(hd(hd(adx(cons(y0, y1))))) -> c16(MARK(hd(adx(cons(y0, y1))))) MARK(hd(hd(incr(nats)))) -> c16(MARK(hd(incr(nats)))) MARK(hd(hd(incr(zeros)))) -> c16(MARK(hd(incr(zeros)))) MARK(hd(hd(cons(adx(y0), y1)))) -> c16(MARK(hd(cons(adx(y0), y1)))) MARK(hd(hd(cons(incr(y0), y1)))) -> c16(MARK(hd(cons(incr(y0), y1)))) MARK(hd(hd(cons(hd(cons(y0, y1)), y2)))) -> c16(MARK(hd(cons(hd(cons(y0, y1)), y2)))) MARK(hd(hd(cons(tl(cons(y0, y1)), y2)))) -> c16(MARK(hd(cons(tl(cons(y0, y1)), y2)))) MARK(hd(hd(cons(hd(adx(nats)), y0)))) -> c16(MARK(hd(cons(hd(adx(nats)), y0)))) MARK(hd(hd(cons(hd(adx(adx(y0))), y1)))) -> c16(MARK(hd(cons(hd(adx(adx(y0))), y1)))) MARK(hd(hd(cons(hd(adx(zeros)), y0)))) -> c16(MARK(hd(cons(hd(adx(zeros)), y0)))) MARK(hd(hd(cons(hd(adx(incr(y0))), y1)))) -> c16(MARK(hd(cons(hd(adx(incr(y0))), y1)))) MARK(hd(hd(cons(hd(adx(hd(y0))), y1)))) -> c16(MARK(hd(cons(hd(adx(hd(y0))), y1)))) MARK(hd(hd(cons(hd(adx(tl(y0))), y1)))) -> c16(MARK(hd(cons(hd(adx(tl(y0))), y1)))) MARK(hd(hd(cons(hd(adx(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(hd(adx(cons(y0, y1))), y2)))) MARK(hd(hd(cons(hd(adx(y0)), y1)))) -> c16(MARK(hd(cons(hd(adx(y0)), y1)))) MARK(hd(hd(cons(hd(incr(nats)), y0)))) -> c16(MARK(hd(cons(hd(incr(nats)), y0)))) MARK(hd(hd(cons(hd(incr(adx(y0))), y1)))) -> c16(MARK(hd(cons(hd(incr(adx(y0))), y1)))) MARK(hd(hd(cons(hd(incr(zeros)), y0)))) -> c16(MARK(hd(cons(hd(incr(zeros)), y0)))) MARK(hd(hd(cons(hd(incr(incr(y0))), y1)))) -> c16(MARK(hd(cons(hd(incr(incr(y0))), y1)))) MARK(hd(hd(cons(hd(incr(hd(y0))), y1)))) -> c16(MARK(hd(cons(hd(incr(hd(y0))), y1)))) MARK(hd(hd(cons(hd(incr(tl(y0))), y1)))) -> c16(MARK(hd(cons(hd(incr(tl(y0))), y1)))) MARK(hd(hd(cons(hd(incr(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(hd(incr(cons(y0, y1))), y2)))) MARK(hd(hd(cons(hd(incr(y0)), y1)))) -> c16(MARK(hd(cons(hd(incr(y0)), y1)))) MARK(hd(hd(cons(hd(hd(nats)), y0)))) -> c16(MARK(hd(cons(hd(hd(nats)), y0)))) MARK(hd(hd(cons(hd(hd(adx(y0))), y1)))) -> c16(MARK(hd(cons(hd(hd(adx(y0))), y1)))) MARK(hd(hd(cons(hd(hd(zeros)), y0)))) -> c16(MARK(hd(cons(hd(hd(zeros)), y0)))) MARK(hd(hd(cons(hd(hd(incr(y0))), y1)))) -> c16(MARK(hd(cons(hd(hd(incr(y0))), y1)))) MARK(hd(hd(cons(hd(hd(hd(y0))), y1)))) -> c16(MARK(hd(cons(hd(hd(hd(y0))), y1)))) MARK(hd(hd(cons(hd(hd(tl(y0))), y1)))) -> c16(MARK(hd(cons(hd(hd(tl(y0))), y1)))) MARK(hd(hd(cons(hd(hd(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(hd(hd(cons(y0, y1))), y2)))) MARK(hd(hd(cons(hd(hd(y0)), y1)))) -> c16(MARK(hd(cons(hd(hd(y0)), y1)))) MARK(hd(hd(cons(hd(tl(nats)), y0)))) -> c16(MARK(hd(cons(hd(tl(nats)), y0)))) MARK(hd(hd(cons(hd(tl(adx(y0))), y1)))) -> c16(MARK(hd(cons(hd(tl(adx(y0))), y1)))) MARK(hd(hd(cons(hd(tl(zeros)), y0)))) -> c16(MARK(hd(cons(hd(tl(zeros)), y0)))) MARK(hd(hd(cons(hd(tl(incr(y0))), y1)))) -> c16(MARK(hd(cons(hd(tl(incr(y0))), y1)))) MARK(hd(hd(cons(hd(tl(hd(y0))), y1)))) -> c16(MARK(hd(cons(hd(tl(hd(y0))), y1)))) MARK(hd(hd(cons(hd(tl(tl(y0))), y1)))) -> c16(MARK(hd(cons(hd(tl(tl(y0))), y1)))) MARK(hd(hd(cons(hd(tl(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(hd(tl(cons(y0, y1))), y2)))) MARK(hd(hd(cons(hd(tl(y0)), y1)))) -> c16(MARK(hd(cons(hd(tl(y0)), y1)))) MARK(hd(hd(cons(hd(nats), y0)))) -> c16(MARK(hd(cons(hd(nats), y0)))) MARK(hd(hd(cons(tl(adx(nats)), y0)))) -> c16(MARK(hd(cons(tl(adx(nats)), y0)))) MARK(hd(hd(cons(tl(adx(adx(y0))), y1)))) -> c16(MARK(hd(cons(tl(adx(adx(y0))), y1)))) MARK(hd(hd(cons(tl(adx(zeros)), y0)))) -> c16(MARK(hd(cons(tl(adx(zeros)), y0)))) MARK(hd(hd(cons(tl(adx(incr(y0))), y1)))) -> c16(MARK(hd(cons(tl(adx(incr(y0))), y1)))) MARK(hd(hd(cons(tl(adx(hd(y0))), y1)))) -> c16(MARK(hd(cons(tl(adx(hd(y0))), y1)))) MARK(hd(hd(cons(tl(adx(tl(y0))), y1)))) -> c16(MARK(hd(cons(tl(adx(tl(y0))), y1)))) MARK(hd(hd(cons(tl(adx(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(tl(adx(cons(y0, y1))), y2)))) MARK(hd(hd(cons(tl(adx(0)), y0)))) -> c16(MARK(hd(cons(tl(adx(0)), y0)))) MARK(hd(hd(cons(tl(adx(s(y0))), y1)))) -> c16(MARK(hd(cons(tl(adx(s(y0))), y1)))) MARK(hd(hd(cons(tl(adx(y0)), y1)))) -> c16(MARK(hd(cons(tl(adx(y0)), y1)))) MARK(hd(hd(cons(tl(incr(nats)), y0)))) -> c16(MARK(hd(cons(tl(incr(nats)), y0)))) MARK(hd(hd(cons(tl(incr(adx(y0))), y1)))) -> c16(MARK(hd(cons(tl(incr(adx(y0))), y1)))) MARK(hd(hd(cons(tl(incr(zeros)), y0)))) -> c16(MARK(hd(cons(tl(incr(zeros)), y0)))) MARK(hd(hd(cons(tl(incr(incr(y0))), y1)))) -> c16(MARK(hd(cons(tl(incr(incr(y0))), y1)))) MARK(hd(hd(cons(tl(incr(hd(y0))), y1)))) -> c16(MARK(hd(cons(tl(incr(hd(y0))), y1)))) MARK(hd(hd(cons(tl(incr(tl(y0))), y1)))) -> c16(MARK(hd(cons(tl(incr(tl(y0))), y1)))) MARK(hd(hd(cons(tl(incr(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(tl(incr(cons(y0, y1))), y2)))) MARK(hd(hd(cons(tl(incr(0)), y0)))) -> c16(MARK(hd(cons(tl(incr(0)), y0)))) MARK(hd(hd(cons(tl(incr(s(y0))), y1)))) -> c16(MARK(hd(cons(tl(incr(s(y0))), y1)))) MARK(hd(hd(cons(tl(incr(y0)), y1)))) -> c16(MARK(hd(cons(tl(incr(y0)), y1)))) MARK(hd(hd(cons(tl(hd(nats)), y0)))) -> c16(MARK(hd(cons(tl(hd(nats)), y0)))) MARK(hd(hd(cons(tl(hd(adx(y0))), y1)))) -> c16(MARK(hd(cons(tl(hd(adx(y0))), y1)))) MARK(hd(hd(cons(tl(hd(zeros)), y0)))) -> c16(MARK(hd(cons(tl(hd(zeros)), y0)))) MARK(hd(hd(cons(tl(hd(incr(y0))), y1)))) -> c16(MARK(hd(cons(tl(hd(incr(y0))), y1)))) MARK(hd(hd(cons(tl(hd(hd(y0))), y1)))) -> c16(MARK(hd(cons(tl(hd(hd(y0))), y1)))) MARK(hd(hd(cons(tl(hd(tl(y0))), y1)))) -> c16(MARK(hd(cons(tl(hd(tl(y0))), y1)))) MARK(hd(hd(cons(tl(hd(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(tl(hd(cons(y0, y1))), y2)))) MARK(hd(hd(cons(tl(hd(y0)), y1)))) -> c16(MARK(hd(cons(tl(hd(y0)), y1)))) MARK(hd(hd(cons(tl(tl(nats)), y0)))) -> c16(MARK(hd(cons(tl(tl(nats)), y0)))) MARK(hd(hd(cons(tl(tl(adx(y0))), y1)))) -> c16(MARK(hd(cons(tl(tl(adx(y0))), y1)))) MARK(hd(hd(cons(tl(tl(zeros)), y0)))) -> c16(MARK(hd(cons(tl(tl(zeros)), y0)))) MARK(hd(hd(cons(tl(tl(incr(y0))), y1)))) -> c16(MARK(hd(cons(tl(tl(incr(y0))), y1)))) MARK(hd(hd(cons(tl(tl(hd(y0))), y1)))) -> c16(MARK(hd(cons(tl(tl(hd(y0))), y1)))) MARK(hd(hd(cons(tl(tl(tl(y0))), y1)))) -> c16(MARK(hd(cons(tl(tl(tl(y0))), y1)))) MARK(hd(hd(cons(tl(tl(cons(y0, y1))), y2)))) -> c16(MARK(hd(cons(tl(tl(cons(y0, y1))), y2)))) MARK(hd(hd(cons(tl(tl(y0)), y1)))) -> c16(MARK(hd(cons(tl(tl(y0)), y1)))) MARK(hd(hd(cons(tl(nats), y0)))) -> c16(MARK(hd(cons(tl(nats), y0)))) MARK(hd(hd(cons(hd(adx(0)), y0)))) -> c16(MARK(hd(cons(hd(adx(0)), y0)))) MARK(hd(hd(cons(hd(adx(s(y0))), y1)))) -> c16(MARK(hd(cons(hd(adx(s(y0))), y1)))) MARK(hd(hd(cons(hd(incr(0)), y0)))) -> c16(MARK(hd(cons(hd(incr(0)), y0)))) MARK(hd(hd(cons(hd(incr(s(y0))), y1)))) -> c16(MARK(hd(cons(hd(incr(s(y0))), y1)))) MARK(hd(hd(adx(hd(cons(y0, y1)))))) -> c16(MARK(hd(adx(hd(cons(y0, y1)))))) MARK(hd(hd(adx(tl(cons(y0, y1)))))) -> c16(MARK(hd(adx(tl(cons(y0, y1)))))) MARK(hd(hd(adx(hd(adx(nats)))))) -> c16(MARK(hd(adx(hd(adx(nats)))))) MARK(hd(hd(adx(hd(adx(adx(y0))))))) -> c16(MARK(hd(adx(hd(adx(adx(y0))))))) MARK(hd(hd(adx(hd(adx(zeros)))))) -> c16(MARK(hd(adx(hd(adx(zeros)))))) MARK(hd(hd(adx(hd(adx(incr(y0))))))) -> c16(MARK(hd(adx(hd(adx(incr(y0))))))) MARK(hd(hd(adx(hd(adx(hd(y0))))))) -> c16(MARK(hd(adx(hd(adx(hd(y0))))))) MARK(hd(hd(adx(hd(adx(tl(y0))))))) -> c16(MARK(hd(adx(hd(adx(tl(y0))))))) MARK(hd(hd(adx(hd(adx(cons(y0, y1))))))) -> c16(MARK(hd(adx(hd(adx(cons(y0, y1))))))) MARK(hd(hd(adx(hd(adx(y0)))))) -> c16(MARK(hd(adx(hd(adx(y0)))))) MARK(hd(hd(adx(hd(incr(nats)))))) -> c16(MARK(hd(adx(hd(incr(nats)))))) MARK(hd(hd(adx(hd(incr(adx(y0))))))) -> c16(MARK(hd(adx(hd(incr(adx(y0))))))) MARK(hd(hd(adx(hd(incr(zeros)))))) -> c16(MARK(hd(adx(hd(incr(zeros)))))) MARK(hd(hd(adx(hd(incr(incr(y0))))))) -> c16(MARK(hd(adx(hd(incr(incr(y0))))))) MARK(hd(hd(adx(hd(incr(hd(y0))))))) -> c16(MARK(hd(adx(hd(incr(hd(y0))))))) MARK(hd(hd(adx(hd(incr(tl(y0))))))) -> c16(MARK(hd(adx(hd(incr(tl(y0))))))) MARK(hd(hd(adx(hd(incr(cons(y0, y1))))))) -> c16(MARK(hd(adx(hd(incr(cons(y0, y1))))))) MARK(hd(hd(adx(hd(incr(y0)))))) -> c16(MARK(hd(adx(hd(incr(y0)))))) MARK(hd(hd(adx(hd(hd(nats)))))) -> c16(MARK(hd(adx(hd(hd(nats)))))) MARK(hd(hd(adx(hd(hd(adx(y0))))))) -> c16(MARK(hd(adx(hd(hd(adx(y0))))))) MARK(hd(hd(adx(hd(hd(incr(y0))))))) -> c16(MARK(hd(adx(hd(hd(incr(y0))))))) MARK(hd(hd(adx(hd(hd(hd(y0))))))) -> c16(MARK(hd(adx(hd(hd(hd(y0))))))) MARK(hd(hd(adx(hd(hd(tl(y0))))))) -> c16(MARK(hd(adx(hd(hd(tl(y0))))))) MARK(hd(hd(adx(hd(hd(cons(y0, y1))))))) -> c16(MARK(hd(adx(hd(hd(cons(y0, y1))))))) MARK(hd(hd(adx(hd(hd(y0)))))) -> c16(MARK(hd(adx(hd(hd(y0)))))) MARK(hd(hd(adx(hd(tl(nats)))))) -> c16(MARK(hd(adx(hd(tl(nats)))))) MARK(hd(hd(adx(hd(tl(adx(y0))))))) -> c16(MARK(hd(adx(hd(tl(adx(y0))))))) MARK(hd(hd(adx(hd(tl(incr(y0))))))) -> c16(MARK(hd(adx(hd(tl(incr(y0))))))) MARK(hd(hd(adx(hd(tl(hd(y0))))))) -> c16(MARK(hd(adx(hd(tl(hd(y0))))))) MARK(hd(hd(adx(hd(tl(tl(y0))))))) -> c16(MARK(hd(adx(hd(tl(tl(y0))))))) MARK(hd(hd(adx(hd(tl(cons(y0, y1))))))) -> c16(MARK(hd(adx(hd(tl(cons(y0, y1))))))) MARK(hd(hd(adx(hd(tl(y0)))))) -> c16(MARK(hd(adx(hd(tl(y0)))))) MARK(hd(hd(adx(hd(nats))))) -> c16(MARK(hd(adx(hd(nats))))) MARK(hd(hd(adx(tl(adx(nats)))))) -> c16(MARK(hd(adx(tl(adx(nats)))))) MARK(hd(hd(adx(tl(adx(adx(y0))))))) -> c16(MARK(hd(adx(tl(adx(adx(y0))))))) MARK(hd(hd(adx(tl(adx(zeros)))))) -> c16(MARK(hd(adx(tl(adx(zeros)))))) MARK(hd(hd(adx(tl(adx(incr(y0))))))) -> c16(MARK(hd(adx(tl(adx(incr(y0))))))) MARK(hd(hd(adx(tl(adx(hd(y0))))))) -> c16(MARK(hd(adx(tl(adx(hd(y0))))))) MARK(hd(hd(adx(tl(adx(tl(y0))))))) -> c16(MARK(hd(adx(tl(adx(tl(y0))))))) MARK(hd(hd(adx(tl(adx(cons(y0, y1))))))) -> c16(MARK(hd(adx(tl(adx(cons(y0, y1))))))) MARK(hd(hd(adx(tl(adx(y0)))))) -> c16(MARK(hd(adx(tl(adx(y0)))))) MARK(hd(hd(adx(tl(incr(nats)))))) -> c16(MARK(hd(adx(tl(incr(nats)))))) MARK(hd(hd(adx(tl(incr(adx(y0))))))) -> c16(MARK(hd(adx(tl(incr(adx(y0))))))) MARK(hd(hd(adx(tl(incr(zeros)))))) -> c16(MARK(hd(adx(tl(incr(zeros)))))) MARK(hd(hd(adx(tl(incr(incr(y0))))))) -> c16(MARK(hd(adx(tl(incr(incr(y0))))))) MARK(hd(hd(adx(tl(incr(hd(y0))))))) -> c16(MARK(hd(adx(tl(incr(hd(y0))))))) MARK(hd(hd(adx(tl(incr(tl(y0))))))) -> c16(MARK(hd(adx(tl(incr(tl(y0))))))) MARK(hd(hd(adx(tl(incr(cons(y0, y1))))))) -> c16(MARK(hd(adx(tl(incr(cons(y0, y1))))))) MARK(hd(hd(adx(tl(incr(s(y0))))))) -> c16(MARK(hd(adx(tl(incr(s(y0))))))) MARK(hd(hd(adx(tl(incr(y0)))))) -> c16(MARK(hd(adx(tl(incr(y0)))))) MARK(hd(hd(adx(tl(hd(nats)))))) -> c16(MARK(hd(adx(tl(hd(nats)))))) MARK(hd(hd(adx(tl(hd(adx(y0))))))) -> c16(MARK(hd(adx(tl(hd(adx(y0))))))) MARK(hd(hd(adx(tl(hd(incr(y0))))))) -> c16(MARK(hd(adx(tl(hd(incr(y0))))))) MARK(hd(hd(adx(tl(hd(hd(y0))))))) -> c16(MARK(hd(adx(tl(hd(hd(y0))))))) MARK(hd(hd(adx(tl(hd(tl(y0))))))) -> c16(MARK(hd(adx(tl(hd(tl(y0))))))) MARK(hd(hd(adx(tl(hd(cons(y0, y1))))))) -> c16(MARK(hd(adx(tl(hd(cons(y0, y1))))))) MARK(hd(hd(adx(tl(hd(y0)))))) -> c16(MARK(hd(adx(tl(hd(y0)))))) MARK(hd(hd(adx(tl(tl(nats)))))) -> c16(MARK(hd(adx(tl(tl(nats)))))) MARK(hd(hd(adx(tl(tl(adx(y0))))))) -> c16(MARK(hd(adx(tl(tl(adx(y0))))))) MARK(hd(hd(adx(tl(tl(incr(y0))))))) -> c16(MARK(hd(adx(tl(tl(incr(y0))))))) MARK(hd(hd(adx(tl(tl(hd(y0))))))) -> c16(MARK(hd(adx(tl(tl(hd(y0))))))) MARK(hd(hd(adx(tl(tl(tl(y0))))))) -> c16(MARK(hd(adx(tl(tl(tl(y0))))))) MARK(hd(hd(adx(tl(tl(cons(y0, y1))))))) -> c16(MARK(hd(adx(tl(tl(cons(y0, y1))))))) MARK(hd(hd(adx(tl(tl(y0)))))) -> c16(MARK(hd(adx(tl(tl(y0)))))) MARK(hd(hd(adx(tl(nats))))) -> c16(MARK(hd(adx(tl(nats))))) MARK(hd(hd(adx(hd(adx(0)))))) -> c16(MARK(hd(adx(hd(adx(0)))))) MARK(hd(hd(adx(hd(adx(s(y0))))))) -> c16(MARK(hd(adx(hd(adx(s(y0))))))) MARK(hd(hd(adx(hd(incr(0)))))) -> c16(MARK(hd(adx(hd(incr(0)))))) MARK(hd(hd(adx(hd(incr(s(y0))))))) -> c16(MARK(hd(adx(hd(incr(s(y0))))))) MARK(hd(hd(adx(hd(hd(zeros)))))) -> c16(MARK(hd(adx(hd(hd(zeros)))))) MARK(hd(hd(adx(tl(hd(zeros)))))) -> c16(MARK(hd(adx(tl(hd(zeros)))))) MARK(hd(hd(adx(tl(adx(0)))))) -> c16(MARK(hd(adx(tl(adx(0)))))) MARK(hd(hd(adx(hd(tl(zeros)))))) -> c16(MARK(hd(adx(hd(tl(zeros)))))) MARK(hd(hd(adx(tl(tl(zeros)))))) -> c16(MARK(hd(adx(tl(tl(zeros)))))) MARK(hd(hd(adx(tl(adx(s(y0))))))) -> c16(MARK(hd(adx(tl(adx(s(y0))))))) MARK(hd(hd(adx(tl(incr(0)))))) -> c16(MARK(hd(adx(tl(incr(0)))))) MARK(hd(hd(incr(hd(cons(y0, y1)))))) -> c16(MARK(hd(incr(hd(cons(y0, y1)))))) MARK(hd(hd(incr(tl(cons(y0, y1)))))) -> c16(MARK(hd(incr(tl(cons(y0, y1)))))) MARK(hd(hd(incr(hd(adx(adx(y0))))))) -> c16(MARK(hd(incr(hd(adx(adx(y0))))))) MARK(hd(hd(incr(hd(adx(incr(y0))))))) -> c16(MARK(hd(incr(hd(adx(incr(y0))))))) MARK(hd(hd(incr(hd(adx(hd(y0))))))) -> c16(MARK(hd(incr(hd(adx(hd(y0))))))) MARK(hd(hd(incr(hd(adx(tl(y0))))))) -> c16(MARK(hd(incr(hd(adx(tl(y0))))))) MARK(hd(hd(incr(hd(adx(y0)))))) -> c16(MARK(hd(incr(hd(adx(y0)))))) MARK(hd(hd(incr(hd(incr(nats)))))) -> c16(MARK(hd(incr(hd(incr(nats)))))) MARK(hd(hd(incr(hd(incr(adx(y0))))))) -> c16(MARK(hd(incr(hd(incr(adx(y0))))))) MARK(hd(hd(incr(hd(incr(zeros)))))) -> c16(MARK(hd(incr(hd(incr(zeros)))))) MARK(hd(hd(incr(hd(incr(incr(y0))))))) -> c16(MARK(hd(incr(hd(incr(incr(y0))))))) MARK(hd(hd(incr(hd(incr(hd(y0))))))) -> c16(MARK(hd(incr(hd(incr(hd(y0))))))) MARK(hd(hd(incr(hd(incr(tl(y0))))))) -> c16(MARK(hd(incr(hd(incr(tl(y0))))))) MARK(hd(hd(incr(hd(incr(cons(y0, y1))))))) -> c16(MARK(hd(incr(hd(incr(cons(y0, y1))))))) MARK(hd(hd(incr(hd(incr(y0)))))) -> c16(MARK(hd(incr(hd(incr(y0)))))) MARK(hd(hd(incr(hd(hd(nats)))))) -> c16(MARK(hd(incr(hd(hd(nats)))))) MARK(hd(hd(incr(hd(hd(adx(y0))))))) -> c16(MARK(hd(incr(hd(hd(adx(y0))))))) MARK(hd(hd(incr(hd(hd(incr(y0))))))) -> c16(MARK(hd(incr(hd(hd(incr(y0))))))) MARK(hd(hd(incr(hd(hd(hd(y0))))))) -> c16(MARK(hd(incr(hd(hd(hd(y0))))))) MARK(hd(hd(incr(hd(hd(tl(y0))))))) -> c16(MARK(hd(incr(hd(hd(tl(y0))))))) MARK(hd(hd(incr(hd(hd(cons(y0, y1))))))) -> c16(MARK(hd(incr(hd(hd(cons(y0, y1))))))) MARK(hd(hd(incr(hd(hd(y0)))))) -> c16(MARK(hd(incr(hd(hd(y0)))))) MARK(hd(hd(incr(hd(tl(nats)))))) -> c16(MARK(hd(incr(hd(tl(nats)))))) MARK(hd(hd(incr(hd(tl(adx(y0))))))) -> c16(MARK(hd(incr(hd(tl(adx(y0))))))) MARK(hd(hd(incr(hd(tl(incr(y0))))))) -> c16(MARK(hd(incr(hd(tl(incr(y0))))))) MARK(hd(hd(incr(hd(tl(hd(y0))))))) -> c16(MARK(hd(incr(hd(tl(hd(y0))))))) MARK(hd(hd(incr(hd(tl(tl(y0))))))) -> c16(MARK(hd(incr(hd(tl(tl(y0))))))) MARK(hd(hd(incr(hd(tl(cons(y0, y1))))))) -> c16(MARK(hd(incr(hd(tl(cons(y0, y1))))))) MARK(hd(hd(incr(hd(tl(y0)))))) -> c16(MARK(hd(incr(hd(tl(y0)))))) MARK(hd(hd(incr(hd(nats))))) -> c16(MARK(hd(incr(hd(nats))))) MARK(hd(hd(incr(tl(adx(adx(y0))))))) -> c16(MARK(hd(incr(tl(adx(adx(y0))))))) MARK(hd(hd(incr(tl(adx(incr(y0))))))) -> c16(MARK(hd(incr(tl(adx(incr(y0))))))) MARK(hd(hd(incr(tl(adx(hd(y0))))))) -> c16(MARK(hd(incr(tl(adx(hd(y0))))))) MARK(hd(hd(incr(tl(adx(tl(y0))))))) -> c16(MARK(hd(incr(tl(adx(tl(y0))))))) MARK(hd(hd(incr(tl(adx(y0)))))) -> c16(MARK(hd(incr(tl(adx(y0)))))) MARK(hd(hd(incr(tl(incr(nats)))))) -> c16(MARK(hd(incr(tl(incr(nats)))))) MARK(hd(hd(incr(tl(incr(adx(y0))))))) -> c16(MARK(hd(incr(tl(incr(adx(y0))))))) MARK(hd(hd(incr(tl(incr(zeros)))))) -> c16(MARK(hd(incr(tl(incr(zeros)))))) MARK(hd(hd(incr(tl(incr(incr(y0))))))) -> c16(MARK(hd(incr(tl(incr(incr(y0))))))) MARK(hd(hd(incr(tl(incr(hd(y0))))))) -> c16(MARK(hd(incr(tl(incr(hd(y0))))))) MARK(hd(hd(incr(tl(incr(tl(y0))))))) -> c16(MARK(hd(incr(tl(incr(tl(y0))))))) MARK(hd(hd(incr(tl(incr(cons(y0, y1))))))) -> c16(MARK(hd(incr(tl(incr(cons(y0, y1))))))) MARK(hd(hd(incr(tl(incr(y0)))))) -> c16(MARK(hd(incr(tl(incr(y0)))))) MARK(hd(hd(incr(tl(hd(nats)))))) -> c16(MARK(hd(incr(tl(hd(nats)))))) MARK(hd(hd(incr(tl(hd(adx(y0))))))) -> c16(MARK(hd(incr(tl(hd(adx(y0))))))) MARK(hd(hd(incr(tl(hd(incr(y0))))))) -> c16(MARK(hd(incr(tl(hd(incr(y0))))))) MARK(hd(hd(incr(tl(hd(hd(y0))))))) -> c16(MARK(hd(incr(tl(hd(hd(y0))))))) MARK(hd(hd(incr(tl(hd(tl(y0))))))) -> c16(MARK(hd(incr(tl(hd(tl(y0))))))) MARK(hd(hd(incr(tl(hd(cons(y0, y1))))))) -> c16(MARK(hd(incr(tl(hd(cons(y0, y1))))))) MARK(hd(hd(incr(tl(hd(y0)))))) -> c16(MARK(hd(incr(tl(hd(y0)))))) MARK(hd(hd(incr(tl(tl(nats)))))) -> c16(MARK(hd(incr(tl(tl(nats)))))) MARK(hd(hd(incr(tl(tl(adx(y0))))))) -> c16(MARK(hd(incr(tl(tl(adx(y0))))))) MARK(hd(hd(incr(tl(tl(incr(y0))))))) -> c16(MARK(hd(incr(tl(tl(incr(y0))))))) MARK(hd(hd(incr(tl(tl(hd(y0))))))) -> c16(MARK(hd(incr(tl(tl(hd(y0))))))) MARK(hd(hd(incr(tl(tl(tl(y0))))))) -> c16(MARK(hd(incr(tl(tl(tl(y0))))))) MARK(hd(hd(incr(tl(tl(cons(y0, y1))))))) -> c16(MARK(hd(incr(tl(tl(cons(y0, y1))))))) MARK(hd(hd(incr(tl(tl(y0)))))) -> c16(MARK(hd(incr(tl(tl(y0)))))) MARK(hd(hd(incr(tl(nats))))) -> c16(MARK(hd(incr(tl(nats))))) MARK(hd(hd(incr(hd(incr(0)))))) -> c16(MARK(hd(incr(hd(incr(0)))))) MARK(hd(hd(incr(hd(incr(s(y0))))))) -> c16(MARK(hd(incr(hd(incr(s(y0))))))) MARK(hd(hd(incr(hd(hd(zeros)))))) -> c16(MARK(hd(incr(hd(hd(zeros)))))) MARK(hd(hd(incr(tl(hd(zeros)))))) -> c16(MARK(hd(incr(tl(hd(zeros)))))) MARK(hd(hd(incr(hd(tl(zeros)))))) -> c16(MARK(hd(incr(hd(tl(zeros)))))) MARK(hd(hd(incr(tl(tl(zeros)))))) -> c16(MARK(hd(incr(tl(tl(zeros)))))) MARK(hd(hd(incr(tl(incr(0)))))) -> c16(MARK(hd(incr(tl(incr(0)))))) MARK(hd(hd(incr(adx(adx(y0)))))) -> c16(MARK(hd(incr(adx(adx(y0)))))) MARK(hd(hd(incr(adx(incr(y0)))))) -> c16(MARK(hd(incr(adx(incr(y0)))))) MARK(hd(hd(incr(adx(hd(cons(y0, y1))))))) -> c16(MARK(hd(incr(adx(hd(cons(y0, y1))))))) MARK(hd(hd(incr(adx(tl(cons(y0, y1))))))) -> c16(MARK(hd(incr(adx(tl(cons(y0, y1))))))) MARK(hd(hd(incr(adx(hd(adx(nats))))))) -> c16(MARK(hd(incr(adx(hd(adx(nats))))))) MARK(hd(hd(incr(adx(hd(adx(adx(y0)))))))) -> c16(MARK(hd(incr(adx(hd(adx(adx(y0)))))))) MARK(hd(hd(incr(adx(hd(adx(zeros))))))) -> c16(MARK(hd(incr(adx(hd(adx(zeros))))))) MARK(hd(hd(incr(adx(hd(adx(incr(y0)))))))) -> c16(MARK(hd(incr(adx(hd(adx(incr(y0)))))))) MARK(hd(hd(incr(adx(hd(adx(hd(y0)))))))) -> c16(MARK(hd(incr(adx(hd(adx(hd(y0)))))))) MARK(hd(hd(incr(adx(hd(adx(tl(y0)))))))) -> c16(MARK(hd(incr(adx(hd(adx(tl(y0)))))))) MARK(hd(hd(incr(adx(hd(adx(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(hd(adx(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(hd(adx(y0))))))) -> c16(MARK(hd(incr(adx(hd(adx(y0))))))) MARK(hd(hd(incr(adx(hd(incr(nats))))))) -> c16(MARK(hd(incr(adx(hd(incr(nats))))))) MARK(hd(hd(incr(adx(hd(incr(adx(y0)))))))) -> c16(MARK(hd(incr(adx(hd(incr(adx(y0)))))))) MARK(hd(hd(incr(adx(hd(incr(zeros))))))) -> c16(MARK(hd(incr(adx(hd(incr(zeros))))))) MARK(hd(hd(incr(adx(hd(incr(incr(y0)))))))) -> c16(MARK(hd(incr(adx(hd(incr(incr(y0)))))))) MARK(hd(hd(incr(adx(hd(incr(hd(y0)))))))) -> c16(MARK(hd(incr(adx(hd(incr(hd(y0)))))))) MARK(hd(hd(incr(adx(hd(incr(tl(y0)))))))) -> c16(MARK(hd(incr(adx(hd(incr(tl(y0)))))))) MARK(hd(hd(incr(adx(hd(incr(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(hd(incr(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(hd(incr(y0))))))) -> c16(MARK(hd(incr(adx(hd(incr(y0))))))) MARK(hd(hd(incr(adx(hd(hd(nats))))))) -> c16(MARK(hd(incr(adx(hd(hd(nats))))))) MARK(hd(hd(incr(adx(hd(hd(adx(y0)))))))) -> c16(MARK(hd(incr(adx(hd(hd(adx(y0)))))))) MARK(hd(hd(incr(adx(hd(hd(incr(y0)))))))) -> c16(MARK(hd(incr(adx(hd(hd(incr(y0)))))))) MARK(hd(hd(incr(adx(hd(hd(hd(y0)))))))) -> c16(MARK(hd(incr(adx(hd(hd(hd(y0)))))))) MARK(hd(hd(incr(adx(hd(hd(tl(y0)))))))) -> c16(MARK(hd(incr(adx(hd(hd(tl(y0)))))))) MARK(hd(hd(incr(adx(hd(hd(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(hd(hd(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(hd(hd(y0))))))) -> c16(MARK(hd(incr(adx(hd(hd(y0))))))) MARK(hd(hd(incr(adx(hd(tl(nats))))))) -> c16(MARK(hd(incr(adx(hd(tl(nats))))))) MARK(hd(hd(incr(adx(hd(tl(adx(y0)))))))) -> c16(MARK(hd(incr(adx(hd(tl(adx(y0)))))))) MARK(hd(hd(incr(adx(hd(tl(incr(y0)))))))) -> c16(MARK(hd(incr(adx(hd(tl(incr(y0)))))))) MARK(hd(hd(incr(adx(hd(tl(hd(y0)))))))) -> c16(MARK(hd(incr(adx(hd(tl(hd(y0)))))))) MARK(hd(hd(incr(adx(hd(tl(tl(y0)))))))) -> c16(MARK(hd(incr(adx(hd(tl(tl(y0)))))))) MARK(hd(hd(incr(adx(hd(tl(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(hd(tl(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(hd(tl(y0))))))) -> c16(MARK(hd(incr(adx(hd(tl(y0))))))) MARK(hd(hd(incr(adx(hd(nats)))))) -> c16(MARK(hd(incr(adx(hd(nats)))))) MARK(hd(hd(incr(adx(tl(adx(nats))))))) -> c16(MARK(hd(incr(adx(tl(adx(nats))))))) MARK(hd(hd(incr(adx(tl(adx(adx(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(adx(y0)))))))) MARK(hd(hd(incr(adx(tl(adx(zeros))))))) -> c16(MARK(hd(incr(adx(tl(adx(zeros))))))) MARK(hd(hd(incr(adx(tl(adx(incr(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(incr(y0)))))))) MARK(hd(hd(incr(adx(tl(adx(hd(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(hd(y0)))))))) MARK(hd(hd(incr(adx(tl(adx(tl(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(tl(y0)))))))) MARK(hd(hd(incr(adx(tl(adx(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(tl(adx(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(tl(adx(y0))))))) -> c16(MARK(hd(incr(adx(tl(adx(y0))))))) MARK(hd(hd(incr(adx(tl(incr(nats))))))) -> c16(MARK(hd(incr(adx(tl(incr(nats))))))) MARK(hd(hd(incr(adx(tl(incr(adx(y0)))))))) -> c16(MARK(hd(incr(adx(tl(incr(adx(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(zeros))))))) -> c16(MARK(hd(incr(adx(tl(incr(zeros))))))) MARK(hd(hd(incr(adx(tl(incr(incr(y0)))))))) -> c16(MARK(hd(incr(adx(tl(incr(incr(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(hd(y0)))))))) -> c16(MARK(hd(incr(adx(tl(incr(hd(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(tl(y0)))))))) -> c16(MARK(hd(incr(adx(tl(incr(tl(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(tl(incr(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(tl(incr(s(y0)))))))) -> c16(MARK(hd(incr(adx(tl(incr(s(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(y0))))))) -> c16(MARK(hd(incr(adx(tl(incr(y0))))))) MARK(hd(hd(incr(adx(tl(hd(nats))))))) -> c16(MARK(hd(incr(adx(tl(hd(nats))))))) MARK(hd(hd(incr(adx(tl(hd(adx(y0)))))))) -> c16(MARK(hd(incr(adx(tl(hd(adx(y0)))))))) MARK(hd(hd(incr(adx(tl(hd(incr(y0)))))))) -> c16(MARK(hd(incr(adx(tl(hd(incr(y0)))))))) MARK(hd(hd(incr(adx(tl(hd(hd(y0)))))))) -> c16(MARK(hd(incr(adx(tl(hd(hd(y0)))))))) MARK(hd(hd(incr(adx(tl(hd(tl(y0)))))))) -> c16(MARK(hd(incr(adx(tl(hd(tl(y0)))))))) MARK(hd(hd(incr(adx(tl(hd(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(tl(hd(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(tl(hd(y0))))))) -> c16(MARK(hd(incr(adx(tl(hd(y0))))))) MARK(hd(hd(incr(adx(tl(tl(nats))))))) -> c16(MARK(hd(incr(adx(tl(tl(nats))))))) MARK(hd(hd(incr(adx(tl(tl(adx(y0)))))))) -> c16(MARK(hd(incr(adx(tl(tl(adx(y0)))))))) MARK(hd(hd(incr(adx(tl(tl(incr(y0)))))))) -> c16(MARK(hd(incr(adx(tl(tl(incr(y0)))))))) MARK(hd(hd(incr(adx(tl(tl(hd(y0)))))))) -> c16(MARK(hd(incr(adx(tl(tl(hd(y0)))))))) MARK(hd(hd(incr(adx(tl(tl(tl(y0)))))))) -> c16(MARK(hd(incr(adx(tl(tl(tl(y0)))))))) MARK(hd(hd(incr(adx(tl(tl(cons(y0, y1)))))))) -> c16(MARK(hd(incr(adx(tl(tl(cons(y0, y1)))))))) MARK(hd(hd(incr(adx(tl(tl(y0))))))) -> c16(MARK(hd(incr(adx(tl(tl(y0))))))) MARK(hd(hd(incr(adx(tl(nats)))))) -> c16(MARK(hd(incr(adx(tl(nats)))))) MARK(hd(hd(incr(adx(hd(adx(0))))))) -> c16(MARK(hd(incr(adx(hd(adx(0))))))) MARK(hd(hd(incr(adx(hd(adx(s(y0)))))))) -> c16(MARK(hd(incr(adx(hd(adx(s(y0)))))))) MARK(hd(hd(incr(adx(hd(incr(0))))))) -> c16(MARK(hd(incr(adx(hd(incr(0))))))) MARK(hd(hd(incr(adx(hd(incr(s(y0)))))))) -> c16(MARK(hd(incr(adx(hd(incr(s(y0)))))))) MARK(hd(hd(incr(adx(hd(hd(zeros))))))) -> c16(MARK(hd(incr(adx(hd(hd(zeros))))))) MARK(hd(hd(incr(adx(tl(hd(zeros))))))) -> c16(MARK(hd(incr(adx(tl(hd(zeros))))))) MARK(hd(hd(incr(adx(tl(adx(0))))))) -> c16(MARK(hd(incr(adx(tl(adx(0))))))) MARK(hd(hd(incr(adx(hd(tl(zeros))))))) -> c16(MARK(hd(incr(adx(hd(tl(zeros))))))) MARK(hd(hd(incr(adx(tl(tl(zeros))))))) -> c16(MARK(hd(incr(adx(tl(tl(zeros))))))) MARK(hd(hd(incr(adx(tl(adx(s(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(s(y0)))))))) MARK(hd(hd(incr(adx(tl(incr(0))))))) -> c16(MARK(hd(incr(adx(tl(incr(0))))))) MARK(hd(hd(incr(hd(adx(nats)))))) -> c16(MARK(hd(incr(hd(adx(nats)))))) MARK(hd(hd(incr(hd(adx(zeros)))))) -> c16(MARK(hd(incr(hd(adx(zeros)))))) MARK(hd(hd(incr(hd(adx(cons(y0, y1))))))) -> c16(MARK(hd(incr(hd(adx(cons(y0, y1))))))) MARK(hd(hd(incr(tl(adx(nats)))))) -> c16(MARK(hd(incr(tl(adx(nats)))))) MARK(hd(hd(incr(tl(adx(zeros)))))) -> c16(MARK(hd(incr(tl(adx(zeros)))))) MARK(hd(hd(incr(tl(adx(cons(y0, y1))))))) -> c16(MARK(hd(incr(tl(adx(cons(y0, y1))))))) MARK(hd(hd(incr(tl(incr(s(y0))))))) -> c16(MARK(hd(incr(tl(incr(s(y0))))))) K tuples:none Defined Rule Symbols: a__nats, a__zeros, a__incr_1, a__adx_1, a__hd_1, a__tl_1, mark_1 Defined Pair Symbols: MARK_1, A__HD_1, A__TL_1 Compound Symbols: c16_2, c16_1, c17_2, c17_1, c8_1, c10_1, c13_1, c15_1 ---------------------------------------- (215) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (216) 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__nats -> a__adx(a__zeros) [1] a__zeros -> cons(0, zeros) [1] a__incr(cons(X, Y)) -> cons(s(X), incr(Y)) [1] a__adx(cons(X, Y)) -> a__incr(cons(X, adx(Y))) [1] a__hd(cons(X, Y)) -> mark(X) [1] a__tl(cons(X, Y)) -> mark(Y) [1] mark(nats) -> a__nats [1] mark(adx(X)) -> a__adx(mark(X)) [1] mark(zeros) -> a__zeros [1] mark(incr(X)) -> a__incr(mark(X)) [1] mark(hd(X)) -> a__hd(mark(X)) [1] mark(tl(X)) -> a__tl(mark(X)) [1] mark(cons(X1, X2)) -> cons(X1, X2) [1] mark(0) -> 0 [1] mark(s(X)) -> s(X) [1] a__nats -> nats [1] a__adx(X) -> adx(X) [1] a__zeros -> zeros [1] a__incr(X) -> incr(X) [1] a__hd(X) -> hd(X) [1] a__tl(X) -> tl(X) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (217) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (218) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__nats -> a__adx(a__zeros) [1] a__zeros -> cons(0, zeros) [1] a__incr(cons(X, Y)) -> cons(s(X), incr(Y)) [1] a__adx(cons(X, Y)) -> a__incr(cons(X, adx(Y))) [1] a__hd(cons(X, Y)) -> mark(X) [1] a__tl(cons(X, Y)) -> mark(Y) [1] mark(nats) -> a__nats [1] mark(adx(X)) -> a__adx(mark(X)) [1] mark(zeros) -> a__zeros [1] mark(incr(X)) -> a__incr(mark(X)) [1] mark(hd(X)) -> a__hd(mark(X)) [1] mark(tl(X)) -> a__tl(mark(X)) [1] mark(cons(X1, X2)) -> cons(X1, X2) [1] mark(0) -> 0 [1] mark(s(X)) -> s(X) [1] a__nats -> nats [1] a__adx(X) -> adx(X) [1] a__zeros -> zeros [1] a__incr(X) -> incr(X) [1] a__hd(X) -> hd(X) [1] a__tl(X) -> tl(X) [1] The TRS has the following type information: a__nats :: 0:zeros:cons:s:incr:adx:nats:hd:tl a__adx :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl a__zeros :: 0:zeros:cons:s:incr:adx:nats:hd:tl cons :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl 0 :: 0:zeros:cons:s:incr:adx:nats:hd:tl zeros :: 0:zeros:cons:s:incr:adx:nats:hd:tl a__incr :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl s :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl incr :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl adx :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl a__hd :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl mark :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl a__tl :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl nats :: 0:zeros:cons:s:incr:adx:nats:hd:tl hd :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl tl :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl Rewrite Strategy: INNERMOST ---------------------------------------- (219) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: mark_1 a__zeros a__hd_1 a__adx_1 a__nats a__tl_1 a__incr_1 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (220) 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__nats -> a__adx(a__zeros) [1] a__zeros -> cons(0, zeros) [1] a__incr(cons(X, Y)) -> cons(s(X), incr(Y)) [1] a__adx(cons(X, Y)) -> a__incr(cons(X, adx(Y))) [1] a__hd(cons(X, Y)) -> mark(X) [1] a__tl(cons(X, Y)) -> mark(Y) [1] mark(nats) -> a__nats [1] mark(adx(X)) -> a__adx(mark(X)) [1] mark(zeros) -> a__zeros [1] mark(incr(X)) -> a__incr(mark(X)) [1] mark(hd(X)) -> a__hd(mark(X)) [1] mark(tl(X)) -> a__tl(mark(X)) [1] mark(cons(X1, X2)) -> cons(X1, X2) [1] mark(0) -> 0 [1] mark(s(X)) -> s(X) [1] a__nats -> nats [1] a__adx(X) -> adx(X) [1] a__zeros -> zeros [1] a__incr(X) -> incr(X) [1] a__hd(X) -> hd(X) [1] a__tl(X) -> tl(X) [1] The TRS has the following type information: a__nats :: 0:zeros:cons:s:incr:adx:nats:hd:tl a__adx :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl a__zeros :: 0:zeros:cons:s:incr:adx:nats:hd:tl cons :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl 0 :: 0:zeros:cons:s:incr:adx:nats:hd:tl zeros :: 0:zeros:cons:s:incr:adx:nats:hd:tl a__incr :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl s :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl incr :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl adx :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl a__hd :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl mark :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl a__tl :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl nats :: 0:zeros:cons:s:incr:adx:nats:hd:tl hd :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl tl :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl Rewrite Strategy: INNERMOST ---------------------------------------- (221) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (222) 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__nats -> a__adx(cons(0, zeros)) [2] a__nats -> a__adx(zeros) [2] a__zeros -> cons(0, zeros) [1] a__incr(cons(X, Y)) -> cons(s(X), incr(Y)) [1] a__adx(cons(X, Y)) -> a__incr(cons(X, adx(Y))) [1] a__hd(cons(X, Y)) -> mark(X) [1] a__tl(cons(X, Y)) -> mark(Y) [1] mark(nats) -> a__nats [1] mark(adx(nats)) -> a__adx(a__nats) [2] mark(adx(adx(X'))) -> a__adx(a__adx(mark(X'))) [2] mark(adx(zeros)) -> a__adx(a__zeros) [2] mark(adx(incr(X''))) -> a__adx(a__incr(mark(X''))) [2] mark(adx(hd(X3))) -> a__adx(a__hd(mark(X3))) [2] mark(adx(tl(X4))) -> a__adx(a__tl(mark(X4))) [2] mark(adx(cons(X1', X2'))) -> a__adx(cons(X1', X2')) [2] mark(adx(0)) -> a__adx(0) [2] mark(adx(s(X5))) -> a__adx(s(X5)) [2] mark(zeros) -> a__zeros [1] mark(incr(nats)) -> a__incr(a__nats) [2] mark(incr(adx(X6))) -> a__incr(a__adx(mark(X6))) [2] mark(incr(zeros)) -> a__incr(a__zeros) [2] mark(incr(incr(X7))) -> a__incr(a__incr(mark(X7))) [2] mark(incr(hd(X8))) -> a__incr(a__hd(mark(X8))) [2] mark(incr(tl(X9))) -> a__incr(a__tl(mark(X9))) [2] mark(incr(cons(X1'', X2''))) -> a__incr(cons(X1'', X2'')) [2] mark(incr(0)) -> a__incr(0) [2] mark(incr(s(X10))) -> a__incr(s(X10)) [2] mark(hd(nats)) -> a__hd(a__nats) [2] mark(hd(adx(X11))) -> a__hd(a__adx(mark(X11))) [2] mark(hd(zeros)) -> a__hd(a__zeros) [2] mark(hd(incr(X12))) -> a__hd(a__incr(mark(X12))) [2] mark(hd(hd(X13))) -> a__hd(a__hd(mark(X13))) [2] mark(hd(tl(X14))) -> a__hd(a__tl(mark(X14))) [2] mark(hd(cons(X15, X21))) -> a__hd(cons(X15, X21)) [2] mark(hd(0)) -> a__hd(0) [2] mark(hd(s(X16))) -> a__hd(s(X16)) [2] mark(tl(nats)) -> a__tl(a__nats) [2] mark(tl(adx(X17))) -> a__tl(a__adx(mark(X17))) [2] mark(tl(zeros)) -> a__tl(a__zeros) [2] mark(tl(incr(X18))) -> a__tl(a__incr(mark(X18))) [2] mark(tl(hd(X19))) -> a__tl(a__hd(mark(X19))) [2] mark(tl(tl(X20))) -> a__tl(a__tl(mark(X20))) [2] mark(tl(cons(X110, X22))) -> a__tl(cons(X110, X22)) [2] mark(tl(0)) -> a__tl(0) [2] mark(tl(s(X23))) -> a__tl(s(X23)) [2] mark(cons(X1, X2)) -> cons(X1, X2) [1] mark(0) -> 0 [1] mark(s(X)) -> s(X) [1] a__nats -> nats [1] a__adx(X) -> adx(X) [1] a__zeros -> zeros [1] a__incr(X) -> incr(X) [1] a__hd(X) -> hd(X) [1] a__tl(X) -> tl(X) [1] The TRS has the following type information: a__nats :: 0:zeros:cons:s:incr:adx:nats:hd:tl a__adx :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl a__zeros :: 0:zeros:cons:s:incr:adx:nats:hd:tl cons :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl 0 :: 0:zeros:cons:s:incr:adx:nats:hd:tl zeros :: 0:zeros:cons:s:incr:adx:nats:hd:tl a__incr :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl s :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl incr :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl adx :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl a__hd :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl mark :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl a__tl :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl nats :: 0:zeros:cons:s:incr:adx:nats:hd:tl hd :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl tl :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl Rewrite Strategy: INNERMOST ---------------------------------------- (223) 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 => 2 nats => 1 ---------------------------------------- (224) Obligation: Complexity RNTS consisting of the following rules: a__adx(z) -{ 1 }-> a__incr(1 + X + (1 + Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 a__adx(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__hd(z) -{ 1 }-> mark(X) :|: Y >= 0, z = 1 + X + Y, X >= 0 a__hd(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__incr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__incr(z) -{ 1 }-> 1 + (1 + X) + (1 + Y) :|: Y >= 0, z = 1 + X + Y, X >= 0 a__nats -{ 2 }-> a__adx(2) :|: a__nats -{ 2 }-> a__adx(1 + 0 + 2) :|: a__nats -{ 1 }-> 1 :|: a__tl(z) -{ 1 }-> mark(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0 a__tl(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__zeros -{ 1 }-> 2 :|: a__zeros -{ 1 }-> 1 + 0 + 2 :|: mark(z) -{ 1 }-> a__zeros :|: z = 2 mark(z) -{ 2 }-> a__tl(a__zeros) :|: z = 1 + 2 mark(z) -{ 2 }-> a__tl(a__tl(mark(X20))) :|: z = 1 + (1 + X20), X20 >= 0 mark(z) -{ 2 }-> a__tl(a__nats) :|: z = 1 + 1 mark(z) -{ 2 }-> a__tl(a__incr(mark(X18))) :|: X18 >= 0, z = 1 + (1 + X18) mark(z) -{ 2 }-> a__tl(a__hd(mark(X19))) :|: X19 >= 0, z = 1 + (1 + X19) mark(z) -{ 2 }-> a__tl(a__adx(mark(X17))) :|: X17 >= 0, z = 1 + (1 + X17) mark(z) -{ 2 }-> a__tl(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__tl(1 + X23) :|: z = 1 + (1 + X23), X23 >= 0 mark(z) -{ 2 }-> a__tl(1 + X110 + X22) :|: X110 >= 0, X22 >= 0, z = 1 + (1 + X110 + X22) mark(z) -{ 1 }-> a__nats :|: z = 1 mark(z) -{ 2 }-> a__incr(a__zeros) :|: z = 1 + 2 mark(z) -{ 2 }-> a__incr(a__tl(mark(X9))) :|: X9 >= 0, z = 1 + (1 + X9) mark(z) -{ 2 }-> a__incr(a__nats) :|: z = 1 + 1 mark(z) -{ 2 }-> a__incr(a__incr(mark(X7))) :|: X7 >= 0, z = 1 + (1 + X7) mark(z) -{ 2 }-> a__incr(a__hd(mark(X8))) :|: X8 >= 0, z = 1 + (1 + X8) mark(z) -{ 2 }-> a__incr(a__adx(mark(X6))) :|: X6 >= 0, z = 1 + (1 + X6) mark(z) -{ 2 }-> a__incr(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__incr(1 + X10) :|: z = 1 + (1 + X10), X10 >= 0 mark(z) -{ 2 }-> a__incr(1 + X1'' + X2'') :|: X1'' >= 0, z = 1 + (1 + X1'' + X2''), X2'' >= 0 mark(z) -{ 2 }-> a__hd(a__zeros) :|: z = 1 + 2 mark(z) -{ 2 }-> a__hd(a__tl(mark(X14))) :|: z = 1 + (1 + X14), X14 >= 0 mark(z) -{ 2 }-> a__hd(a__nats) :|: z = 1 + 1 mark(z) -{ 2 }-> a__hd(a__incr(mark(X12))) :|: z = 1 + (1 + X12), X12 >= 0 mark(z) -{ 2 }-> a__hd(a__hd(mark(X13))) :|: z = 1 + (1 + X13), X13 >= 0 mark(z) -{ 2 }-> a__hd(a__adx(mark(X11))) :|: X11 >= 0, z = 1 + (1 + X11) mark(z) -{ 2 }-> a__hd(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__hd(1 + X16) :|: X16 >= 0, z = 1 + (1 + X16) mark(z) -{ 2 }-> a__hd(1 + X15 + X21) :|: X21 >= 0, z = 1 + (1 + X15 + X21), X15 >= 0 mark(z) -{ 2 }-> a__adx(a__zeros) :|: z = 1 + 2 mark(z) -{ 2 }-> a__adx(a__tl(mark(X4))) :|: z = 1 + (1 + X4), X4 >= 0 mark(z) -{ 2 }-> a__adx(a__nats) :|: z = 1 + 1 mark(z) -{ 2 }-> a__adx(a__incr(mark(X''))) :|: z = 1 + (1 + X''), X'' >= 0 mark(z) -{ 2 }-> a__adx(a__hd(mark(X3))) :|: z = 1 + (1 + X3), X3 >= 0 mark(z) -{ 2 }-> a__adx(a__adx(mark(X'))) :|: X' >= 0, z = 1 + (1 + X') mark(z) -{ 2 }-> a__adx(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__adx(1 + X5) :|: X5 >= 0, z = 1 + (1 + X5) mark(z) -{ 2 }-> a__adx(1 + X1' + X2') :|: z = 1 + (1 + X1' + X2'), X2' >= 0, X1' >= 0 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + X :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (225) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__zeros -{ 1 }-> 1 + 0 + 2 :|: a__zeros -{ 1 }-> 2 :|: a__incr(z) -{ 1 }-> 1 + (1 + X) + (1 + Y) :|: Y >= 0, z = 1 + X + Y, X >= 0 a__incr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__adx(z) -{ 1 }-> a__incr(1 + X + (1 + Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 a__adx(z) -{ 1 }-> 1 + X :|: X >= 0, z = X ---------------------------------------- (226) Obligation: Complexity RNTS consisting of the following rules: a__adx(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__adx(z) -{ 2 }-> 1 + X' :|: Y >= 0, z = 1 + X + Y, X >= 0, X' >= 0, 1 + X + (1 + Y) = X' a__adx(z) -{ 2 }-> 1 + (1 + X') + (1 + Y') :|: Y >= 0, z = 1 + X + Y, X >= 0, Y' >= 0, 1 + X + (1 + Y) = 1 + X' + Y', X' >= 0 a__hd(z) -{ 1 }-> mark(X) :|: Y >= 0, z = 1 + X + Y, X >= 0 a__hd(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__incr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__incr(z) -{ 1 }-> 1 + (1 + X) + (1 + Y) :|: Y >= 0, z = 1 + X + Y, X >= 0 a__nats -{ 3 }-> a__incr(1 + X + (1 + Y)) :|: Y >= 0, 1 + 0 + 2 = 1 + X + Y, X >= 0 a__nats -{ 3 }-> a__incr(1 + X + (1 + Y)) :|: Y >= 0, 2 = 1 + X + Y, X >= 0 a__nats -{ 1 }-> 1 :|: a__nats -{ 3 }-> 1 + X :|: X >= 0, 1 + 0 + 2 = X a__nats -{ 3 }-> 1 + X :|: X >= 0, 2 = X a__tl(z) -{ 1 }-> mark(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0 a__tl(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__zeros -{ 1 }-> 2 :|: a__zeros -{ 1 }-> 1 + 0 + 2 :|: mark(z) -{ 2 }-> a__tl(a__tl(mark(X20))) :|: z = 1 + (1 + X20), X20 >= 0 mark(z) -{ 2 }-> a__tl(a__nats) :|: z = 1 + 1 mark(z) -{ 2 }-> a__tl(a__incr(mark(X18))) :|: X18 >= 0, z = 1 + (1 + X18) mark(z) -{ 2 }-> a__tl(a__hd(mark(X19))) :|: X19 >= 0, z = 1 + (1 + X19) mark(z) -{ 2 }-> a__tl(a__adx(mark(X17))) :|: X17 >= 0, z = 1 + (1 + X17) mark(z) -{ 3 }-> a__tl(2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__tl(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__tl(1 + X23) :|: z = 1 + (1 + X23), X23 >= 0 mark(z) -{ 2 }-> a__tl(1 + X110 + X22) :|: X110 >= 0, X22 >= 0, z = 1 + (1 + X110 + X22) mark(z) -{ 3 }-> a__tl(1 + 0 + 2) :|: z = 1 + 2 mark(z) -{ 1 }-> a__nats :|: z = 1 mark(z) -{ 2 }-> a__incr(a__tl(mark(X9))) :|: X9 >= 0, z = 1 + (1 + X9) mark(z) -{ 2 }-> a__incr(a__nats) :|: z = 1 + 1 mark(z) -{ 2 }-> a__incr(a__incr(mark(X7))) :|: X7 >= 0, z = 1 + (1 + X7) mark(z) -{ 2 }-> a__incr(a__hd(mark(X8))) :|: X8 >= 0, z = 1 + (1 + X8) mark(z) -{ 2 }-> a__incr(a__adx(mark(X6))) :|: X6 >= 0, z = 1 + (1 + X6) mark(z) -{ 3 }-> a__incr(1 + X + (1 + Y)) :|: z = 1 + (1 + X1' + X2'), X2' >= 0, X1' >= 0, Y >= 0, 1 + X1' + X2' = 1 + X + Y, X >= 0 mark(z) -{ 3 }-> a__incr(1 + X + (1 + Y)) :|: X5 >= 0, z = 1 + (1 + X5), Y >= 0, 1 + X5 = 1 + X + Y, X >= 0 mark(z) -{ 4 }-> a__incr(1 + X + (1 + Y)) :|: z = 1 + 2, Y >= 0, 1 + 0 + 2 = 1 + X + Y, X >= 0 mark(z) -{ 4 }-> a__incr(1 + X + (1 + Y)) :|: z = 1 + 2, Y >= 0, 2 = 1 + X + Y, X >= 0 mark(z) -{ 2 }-> a__hd(a__tl(mark(X14))) :|: z = 1 + (1 + X14), X14 >= 0 mark(z) -{ 2 }-> a__hd(a__nats) :|: z = 1 + 1 mark(z) -{ 2 }-> a__hd(a__incr(mark(X12))) :|: z = 1 + (1 + X12), X12 >= 0 mark(z) -{ 2 }-> a__hd(a__hd(mark(X13))) :|: z = 1 + (1 + X13), X13 >= 0 mark(z) -{ 2 }-> a__hd(a__adx(mark(X11))) :|: X11 >= 0, z = 1 + (1 + X11) mark(z) -{ 3 }-> a__hd(2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__hd(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__hd(1 + X16) :|: X16 >= 0, z = 1 + (1 + X16) mark(z) -{ 2 }-> a__hd(1 + X15 + X21) :|: X21 >= 0, z = 1 + (1 + X15 + X21), X15 >= 0 mark(z) -{ 3 }-> a__hd(1 + 0 + 2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__adx(a__tl(mark(X4))) :|: z = 1 + (1 + X4), X4 >= 0 mark(z) -{ 2 }-> a__adx(a__nats) :|: z = 1 + 1 mark(z) -{ 2 }-> a__adx(a__incr(mark(X''))) :|: z = 1 + (1 + X''), X'' >= 0 mark(z) -{ 2 }-> a__adx(a__hd(mark(X3))) :|: z = 1 + (1 + X3), X3 >= 0 mark(z) -{ 2 }-> a__adx(a__adx(mark(X'))) :|: X' >= 0, z = 1 + (1 + X') mark(z) -{ 2 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + X :|: z = 1 + X, X >= 0 mark(z) -{ 3 }-> 1 + X :|: X1'' >= 0, z = 1 + (1 + X1'' + X2''), X2'' >= 0, X >= 0, 1 + X1'' + X2'' = X mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X mark(z) -{ 3 }-> 1 + X :|: z = 1 + (1 + X10), X10 >= 0, X >= 0, 1 + X10 = X mark(z) -{ 4 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 + 0 + 2 = X mark(z) -{ 4 }-> 1 + X :|: z = 1 + 2, X >= 0, 2 = X mark(z) -{ 3 }-> 1 + X :|: z = 1 + (1 + X1' + X2'), X2' >= 0, X1' >= 0, X >= 0, 1 + X1' + X2' = X mark(z) -{ 3 }-> 1 + X :|: X5 >= 0, z = 1 + (1 + X5), X >= 0, 1 + X5 = X mark(z) -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> 1 + 0 + 2 :|: z = 2 mark(z) -{ 3 }-> 1 + (1 + X) + (1 + Y) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2''), X2'' >= 0, Y >= 0, 1 + X1'' + X2'' = 1 + X + Y, X >= 0 mark(z) -{ 3 }-> 1 + (1 + X) + (1 + Y) :|: z = 1 + (1 + X10), X10 >= 0, Y >= 0, 1 + X10 = 1 + X + Y, X >= 0 mark(z) -{ 4 }-> 1 + (1 + X) + (1 + Y) :|: z = 1 + 2, Y >= 0, 1 + 0 + 2 = 1 + X + Y, X >= 0 mark(z) -{ 4 }-> 1 + (1 + X) + (1 + Y) :|: z = 1 + 2, Y >= 0, 2 = 1 + X + Y, X >= 0 ---------------------------------------- (227) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (228) Obligation: Complexity RNTS consisting of the following rules: a__adx(z) -{ 2 }-> 1 + X' :|: Y >= 0, z = 1 + X + Y, X >= 0, X' >= 0, 1 + X + (1 + Y) = X' a__adx(z) -{ 1 }-> 1 + z :|: z >= 0 a__adx(z) -{ 2 }-> 1 + (1 + X') + (1 + Y') :|: Y >= 0, z = 1 + X + Y, X >= 0, Y' >= 0, 1 + X + (1 + Y) = 1 + X' + Y', X' >= 0 a__hd(z) -{ 1 }-> mark(X) :|: Y >= 0, z = 1 + X + Y, X >= 0 a__hd(z) -{ 1 }-> 1 + z :|: z >= 0 a__incr(z) -{ 1 }-> 1 + z :|: z >= 0 a__incr(z) -{ 1 }-> 1 + (1 + X) + (1 + Y) :|: Y >= 0, z = 1 + X + Y, X >= 0 a__nats -{ 3 }-> a__incr(1 + X + (1 + Y)) :|: Y >= 0, 1 + 0 + 2 = 1 + X + Y, X >= 0 a__nats -{ 3 }-> a__incr(1 + X + (1 + Y)) :|: Y >= 0, 2 = 1 + X + Y, X >= 0 a__nats -{ 1 }-> 1 :|: a__nats -{ 3 }-> 1 + X :|: X >= 0, 1 + 0 + 2 = X a__nats -{ 3 }-> 1 + X :|: X >= 0, 2 = X a__tl(z) -{ 1 }-> mark(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0 a__tl(z) -{ 1 }-> 1 + z :|: z >= 0 a__zeros -{ 1 }-> 2 :|: a__zeros -{ 1 }-> 1 + 0 + 2 :|: mark(z) -{ 2 }-> a__tl(a__tl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__tl(a__nats) :|: z = 1 + 1 mark(z) -{ 2 }-> a__tl(a__incr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__tl(a__hd(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__tl(a__adx(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 3 }-> a__tl(2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__tl(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__tl(1 + (z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__tl(1 + X110 + X22) :|: X110 >= 0, X22 >= 0, z = 1 + (1 + X110 + X22) mark(z) -{ 3 }-> a__tl(1 + 0 + 2) :|: z = 1 + 2 mark(z) -{ 1 }-> a__nats :|: z = 1 mark(z) -{ 2 }-> a__incr(a__tl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__incr(a__nats) :|: z = 1 + 1 mark(z) -{ 2 }-> a__incr(a__incr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__incr(a__hd(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__incr(a__adx(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 3 }-> a__incr(1 + X + (1 + Y)) :|: z = 1 + (1 + X1' + X2'), X2' >= 0, X1' >= 0, Y >= 0, 1 + X1' + X2' = 1 + X + Y, X >= 0 mark(z) -{ 3 }-> a__incr(1 + X + (1 + Y)) :|: z - 2 >= 0, Y >= 0, 1 + (z - 2) = 1 + X + Y, X >= 0 mark(z) -{ 4 }-> a__incr(1 + X + (1 + Y)) :|: z = 1 + 2, Y >= 0, 1 + 0 + 2 = 1 + X + Y, X >= 0 mark(z) -{ 4 }-> a__incr(1 + X + (1 + Y)) :|: z = 1 + 2, Y >= 0, 2 = 1 + X + Y, X >= 0 mark(z) -{ 2 }-> a__hd(a__tl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__hd(a__nats) :|: z = 1 + 1 mark(z) -{ 2 }-> a__hd(a__incr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__hd(a__hd(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__hd(a__adx(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 3 }-> a__hd(2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__hd(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__hd(1 + (z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__hd(1 + X15 + X21) :|: X21 >= 0, z = 1 + (1 + X15 + X21), X15 >= 0 mark(z) -{ 3 }-> a__hd(1 + 0 + 2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__adx(a__tl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__adx(a__nats) :|: z = 1 + 1 mark(z) -{ 2 }-> a__adx(a__incr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__adx(a__hd(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__adx(a__adx(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 3 }-> 1 + X :|: X1'' >= 0, z = 1 + (1 + X1'' + X2''), X2'' >= 0, X >= 0, 1 + X1'' + X2'' = X mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X mark(z) -{ 3 }-> 1 + X :|: z - 2 >= 0, X >= 0, 1 + (z - 2) = X mark(z) -{ 4 }-> 1 + X :|: z = 1 + 2, X >= 0, 1 + 0 + 2 = X mark(z) -{ 4 }-> 1 + X :|: z = 1 + 2, X >= 0, 2 = X mark(z) -{ 3 }-> 1 + X :|: z = 1 + (1 + X1' + X2'), X2' >= 0, X1' >= 0, X >= 0, 1 + X1' + X2' = X mark(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> 1 + 0 + 2 :|: z = 2 mark(z) -{ 3 }-> 1 + (1 + X) + (1 + Y) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2''), X2'' >= 0, Y >= 0, 1 + X1'' + X2'' = 1 + X + Y, X >= 0 mark(z) -{ 3 }-> 1 + (1 + X) + (1 + Y) :|: z - 2 >= 0, Y >= 0, 1 + (z - 2) = 1 + X + Y, X >= 0 mark(z) -{ 4 }-> 1 + (1 + X) + (1 + Y) :|: z = 1 + 2, Y >= 0, 1 + 0 + 2 = 1 + X + Y, X >= 0 mark(z) -{ 4 }-> 1 + (1 + X) + (1 + Y) :|: z = 1 + 2, Y >= 0, 2 = 1 + X + Y, X >= 0 ---------------------------------------- (229) 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 ---------------------------------------- (230) 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__nats -> a__adx(a__zeros) [1] a__zeros -> cons(0, zeros) [1] a__incr(cons(X, Y)) -> cons(s(X), incr(Y)) [1] a__adx(cons(X, Y)) -> a__incr(cons(X, adx(Y))) [1] a__hd(cons(X, Y)) -> mark(X) [1] a__tl(cons(X, Y)) -> mark(Y) [1] mark(nats) -> a__nats [1] mark(adx(X)) -> a__adx(mark(X)) [1] mark(zeros) -> a__zeros [1] mark(incr(X)) -> a__incr(mark(X)) [1] mark(hd(X)) -> a__hd(mark(X)) [1] mark(tl(X)) -> a__tl(mark(X)) [1] mark(cons(X1, X2)) -> cons(X1, X2) [1] mark(0) -> 0 [1] mark(s(X)) -> s(X) [1] a__nats -> nats [1] a__adx(X) -> adx(X) [1] a__zeros -> zeros [1] a__incr(X) -> incr(X) [1] a__hd(X) -> hd(X) [1] a__tl(X) -> tl(X) [1] The TRS has the following type information: a__nats :: 0:zeros:cons:s:incr:adx:nats:hd:tl a__adx :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl a__zeros :: 0:zeros:cons:s:incr:adx:nats:hd:tl cons :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl 0 :: 0:zeros:cons:s:incr:adx:nats:hd:tl zeros :: 0:zeros:cons:s:incr:adx:nats:hd:tl a__incr :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl s :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl incr :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl adx :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl a__hd :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl mark :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl a__tl :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl nats :: 0:zeros:cons:s:incr:adx:nats:hd:tl hd :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl tl :: 0:zeros:cons:s:incr:adx:nats:hd:tl -> 0:zeros:cons:s:incr:adx:nats:hd:tl Rewrite Strategy: INNERMOST ---------------------------------------- (231) 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 => 2 nats => 1 ---------------------------------------- (232) Obligation: Complexity RNTS consisting of the following rules: a__adx(z) -{ 1 }-> a__incr(1 + X + (1 + Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 a__adx(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__hd(z) -{ 1 }-> mark(X) :|: Y >= 0, z = 1 + X + Y, X >= 0 a__hd(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__incr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__incr(z) -{ 1 }-> 1 + (1 + X) + (1 + Y) :|: Y >= 0, z = 1 + X + Y, X >= 0 a__nats -{ 1 }-> a__adx(a__zeros) :|: a__nats -{ 1 }-> 1 :|: a__tl(z) -{ 1 }-> mark(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0 a__tl(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__zeros -{ 1 }-> 2 :|: a__zeros -{ 1 }-> 1 + 0 + 2 :|: mark(z) -{ 1 }-> a__zeros :|: z = 2 mark(z) -{ 1 }-> a__tl(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__nats :|: z = 1 mark(z) -{ 1 }-> a__incr(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__hd(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__adx(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + X :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 Only complete derivations are relevant for the runtime complexity.