KILLED proof of input_ipzrDed8rQ.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 3 ms] (14) CpxRNTS (15) InliningProof [UPPER BOUND(ID), 929 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) CompletionProof [UPPER BOUND(ID), 0 ms] (20) CpxTypedWeightedCompleteTrs (21) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (24) CdtProblem (25) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CdtProblem (27) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CdtProblem (31) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CdtProblem (33) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms] (50) CdtProblem (51) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtNarrowingProof [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) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) 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), 0 ms] (74) CdtProblem (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 61 ms] (90) CdtProblem (91) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 88 ms] (94) CdtProblem (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 104 ms] (98) CdtProblem (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 90 ms] (102) CdtProblem (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 225 ms] (106) CdtProblem (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 164 ms] (110) CdtProblem (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 269 ms] (114) CdtProblem (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 317 ms] (118) CdtProblem (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtRewritingProof [BOTH BOUNDS(ID, ID), 29 ms] (130) CdtProblem (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 3 ms] (138) CdtProblem (139) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtRewritingProof [BOTH BOUNDS(ID, ID), 39 ms] (144) CdtProblem (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 36 ms] (148) CdtProblem (149) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 28 ms] (154) CdtProblem (155) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1155 ms] (160) CdtProblem (161) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtRewritingProof [BOTH BOUNDS(ID, ID), 21 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtRewritingProof [BOTH BOUNDS(ID, ID), 70 ms] (168) CdtProblem (169) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 157 ms] (172) CdtProblem (173) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1308 ms] (178) CdtProblem (179) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 52 ms] (182) CdtProblem (183) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 54 ms] (184) CdtProblem (185) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 15 ms] (186) CdtProblem (187) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 68 ms] (188) CdtProblem (189) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (190) CdtProblem (191) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 170 ms] (192) CdtProblem (193) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 169 ms] (194) CdtProblem (195) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (196) CdtProblem (197) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 1931 ms] (198) CdtProblem ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__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) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) 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 ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) 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 ---------------------------------------- (9) 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 ---------------------------------------- (10) 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 ---------------------------------------- (11) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (12) 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 ---------------------------------------- (13) 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 ---------------------------------------- (14) 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 ---------------------------------------- (15) 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 ---------------------------------------- (16) 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 ---------------------------------------- (17) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (18) 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 ---------------------------------------- (19) 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 ---------------------------------------- (20) 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 ---------------------------------------- (21) 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 ---------------------------------------- (22) 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. ---------------------------------------- (23) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (24) 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 ---------------------------------------- (25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 15 trailing nodes: A__ADX(cons(z0, z1)) -> c6(A__INCR(cons(z0, adx(z1)))) MARK(zeros) -> c14(A__ZEROS) A__TL(z0) -> c11 A__ZEROS -> c2 MARK(0) -> c19 A__NATS -> c(A__ADX(a__zeros), A__ZEROS) MARK(s(z0)) -> c20 A__ZEROS -> c3 A__NATS -> c1 MARK(cons(z0, z1)) -> c18 A__INCR(z0) -> c5 A__ADX(z0) -> c7 A__INCR(cons(z0, z1)) -> c4 A__HD(z0) -> c9 MARK(nats) -> c12(A__NATS) ---------------------------------------- (26) 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 ---------------------------------------- (27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (28) 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 ---------------------------------------- (29) 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))) ---------------------------------------- (30) 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 ---------------------------------------- (31) 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)) ---------------------------------------- (32) 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 ---------------------------------------- (33) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (34) 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 ---------------------------------------- (35) 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))) ---------------------------------------- (36) 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 ---------------------------------------- (37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(tl(0)) -> c17(A__TL(0), MARK(0)) MARK(tl(s(z0))) -> c17(A__TL(s(z0)), MARK(s(z0))) ---------------------------------------- (38) 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 ---------------------------------------- (39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (40) 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 ---------------------------------------- (41) 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))) ---------------------------------------- (42) 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 ---------------------------------------- (43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (44) 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 ---------------------------------------- (45) 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))) ---------------------------------------- (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(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 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (49) 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)))) ---------------------------------------- (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(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 ---------------------------------------- (51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (53) 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)))) ---------------------------------------- (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(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 ---------------------------------------- (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(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 ---------------------------------------- (57) 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)) ---------------------------------------- (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(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 ---------------------------------------- (59) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(hd(nats)) -> c16(A__HD(nats)) ---------------------------------------- (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(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 ---------------------------------------- (61) 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)) ---------------------------------------- (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(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 ---------------------------------------- (63) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(hd(zeros)) -> c16(A__HD(zeros)) ---------------------------------------- (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(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 ---------------------------------------- (65) 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))) ---------------------------------------- (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(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 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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(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 ---------------------------------------- (69) 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))) ---------------------------------------- (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(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 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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(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 ---------------------------------------- (73) 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)))) ---------------------------------------- (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(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 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (77) 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)))) ---------------------------------------- (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(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 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (81) 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)) ---------------------------------------- (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(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 ---------------------------------------- (83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(tl(nats)) -> c17(A__TL(nats)) ---------------------------------------- (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(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 ---------------------------------------- (85) 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)) ---------------------------------------- (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(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 ---------------------------------------- (87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(tl(zeros)) -> c17(A__TL(zeros)) ---------------------------------------- (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(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 ---------------------------------------- (89) 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))) ---------------------------------------- (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(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 ---------------------------------------- (91) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(hd(hd(0))) -> c16(A__HD(hd(0))) ---------------------------------------- (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(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 ---------------------------------------- (93) 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)))) ---------------------------------------- (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(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 ---------------------------------------- (95) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(hd(hd(s(x0)))) -> c16(A__HD(hd(s(x0)))) ---------------------------------------- (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(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 ---------------------------------------- (97) 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))) ---------------------------------------- (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(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 ---------------------------------------- (99) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(hd(tl(0))) -> c16(A__HD(tl(0))) ---------------------------------------- (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(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 ---------------------------------------- (101) 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)))) ---------------------------------------- (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(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 ---------------------------------------- (103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(hd(tl(s(x0)))) -> c16(A__HD(tl(s(x0)))) ---------------------------------------- (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(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 ---------------------------------------- (105) 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))) ---------------------------------------- (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(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 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(tl(hd(0))) -> c17(A__TL(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(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 ---------------------------------------- (109) 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)))) ---------------------------------------- (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(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 ---------------------------------------- (111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(tl(hd(s(x0)))) -> c17(A__TL(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(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 ---------------------------------------- (113) 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))) ---------------------------------------- (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(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 ---------------------------------------- (115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(tl(tl(0))) -> c17(A__TL(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(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 ---------------------------------------- (117) 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)))) ---------------------------------------- (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(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 ---------------------------------------- (119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(tl(tl(s(x0)))) -> c17(A__TL(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(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 ---------------------------------------- (121) 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))) ---------------------------------------- (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(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 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (125) 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)))) ---------------------------------------- (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(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 ---------------------------------------- (127) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (129) 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))) ---------------------------------------- (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(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 ---------------------------------------- (131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (133) 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)))) ---------------------------------------- (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(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 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (137) 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))))) ---------------------------------------- (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__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 ---------------------------------------- (139) 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))) ---------------------------------------- (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__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 ---------------------------------------- (141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (143) 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))) ---------------------------------------- (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__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 ---------------------------------------- (145) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (147) 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)))) ---------------------------------------- (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: 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 ---------------------------------------- (149) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(tl(zeros)) -> c17(A__TL(cons(0, zeros))) A__TL(cons(z0, tl(zeros))) -> c10(MARK(tl(zeros))) A__HD(cons(tl(zeros), z1)) -> c8(MARK(tl(zeros))) ---------------------------------------- (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: 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 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 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: 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 ---------------------------------------- (153) 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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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)))) ---------------------------------------- (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: 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))) 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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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)))) 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(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))) 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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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)))) 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 ---------------------------------------- (155) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(hd(adx(s(z0)))) -> c16(MARK(adx(s(z0)))) MARK(tl(adx(0))) -> c17(MARK(adx(0))) MARK(hd(adx(0))) -> c16(MARK(adx(0))) ---------------------------------------- (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: 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(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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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)))) 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(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(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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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)))) 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 ---------------------------------------- (157) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 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: 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(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(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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(adx(s(z0)))) -> c17(A__TL(a__adx(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(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(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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(adx(s(z0)))) -> c17(A__TL(a__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: c15_1, c16_1, c17_1, c16_2, c17_2, c8_1, c10_1, c13_1 ---------------------------------------- (159) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(tl(adx(s(z0)))) -> c17(A__TL(a__adx(s(z0)))) by MARK(tl(adx(s(x0)))) -> c17(A__TL(adx(s(x0)))) ---------------------------------------- (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: 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(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(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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(adx(s(x0)))) -> c17(A__TL(adx(s(x0)))) 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(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(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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(adx(s(x0)))) -> c17(A__TL(adx(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: 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 ---------------------------------------- (161) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(tl(adx(s(x0)))) -> c17(A__TL(adx(s(x0)))) ---------------------------------------- (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: 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(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(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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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 ---------------------------------------- (163) 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))) ---------------------------------------- (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(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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(0))) -> c17(A__TL(incr(0)), MARK(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(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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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: c15_1, c16_1, c17_1, c16_2, c17_2, c8_1, c10_1, c13_1 ---------------------------------------- (165) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(0))) -> c17(MARK(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(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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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: c15_1, c16_1, c17_1, c16_2, c17_2, c8_1, c10_1, c13_1 ---------------------------------------- (167) 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)))) ---------------------------------------- (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(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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(0))) -> c17(MARK(incr(0))) 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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(0))) -> c17(MARK(incr(0))) 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 ---------------------------------------- (169) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(0))) -> c17(MARK(incr(0))) 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, 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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(0))) -> c17(MARK(incr(0))) 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 ---------------------------------------- (171) 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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) MARK(incr(tl(incr(s(y0))))) -> c15(MARK(tl(incr(s(y0))))) ---------------------------------------- (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(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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(0))) -> c17(MARK(incr(0))) 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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(0))) -> c17(MARK(incr(0))) 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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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 ---------------------------------------- (173) 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))) ---------------------------------------- (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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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 ---------------------------------------- (175) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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)) -> 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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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 ---------------------------------------- (177) 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)))) ---------------------------------------- (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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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 ---------------------------------------- (179) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(hd(incr(cons(x0, x1)))) -> c16(A__HD(incr(cons(x0, x1)))) MARK(hd(incr(cons(z0, z1)))) -> c16(A__HD(cons(s(z0), incr(z1)))) ---------------------------------------- (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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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 ---------------------------------------- (181) 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))) ---------------------------------------- (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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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 ---------------------------------------- (183) 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))))) ---------------------------------------- (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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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 ---------------------------------------- (185) 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(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c16(MARK(adx(tl(incr(0))))) 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))))) ---------------------------------------- (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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c16(MARK(adx(tl(incr(0))))) 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))))) 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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c16(MARK(adx(tl(incr(0))))) 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))))) 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 ---------------------------------------- (187) 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(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c16(MARK(adx(tl(incr(0))))) 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))))) ---------------------------------------- (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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c16(MARK(adx(tl(incr(0))))) 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))))) 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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c16(MARK(adx(tl(incr(0))))) 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))))) 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 ---------------------------------------- (189) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing nodes: MARK(adx(hd(adx(0)))) -> c13(MARK(hd(adx(0)))) A__TL(cons(z0, hd(adx(s(y0))))) -> c10(MARK(hd(adx(s(y0))))) A__HD(cons(hd(adx(s(y0))), z1)) -> c8(MARK(hd(adx(s(y0))))) A__TL(cons(z0, hd(adx(0)))) -> c10(MARK(hd(adx(0)))) A__HD(cons(hd(adx(0)), z1)) -> c8(MARK(hd(adx(0)))) MARK(adx(hd(adx(s(y0))))) -> c13(MARK(hd(adx(s(y0))))) ---------------------------------------- (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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c16(MARK(adx(tl(incr(0))))) 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))))) 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, 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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c16(MARK(adx(tl(incr(0))))) 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))))) 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 ---------------------------------------- (191) 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(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(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) 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(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) 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(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(0))))) -> c16(MARK(incr(tl(incr(0))))) MARK(hd(incr(tl(incr(s(y0)))))) -> c16(MARK(incr(tl(incr(s(y0)))))) ---------------------------------------- (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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c16(MARK(adx(tl(incr(0))))) 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(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(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(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) 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(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) 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(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(0))))) -> c16(MARK(incr(tl(incr(0))))) 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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c16(MARK(adx(tl(incr(0))))) 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(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(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(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) 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(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) 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(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(0))))) -> c16(MARK(incr(tl(incr(0))))) 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 ---------------------------------------- (193) 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(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(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) 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(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) 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(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(0))))) -> c16(MARK(incr(tl(incr(0))))) MARK(hd(incr(tl(incr(s(y0)))))) -> c16(MARK(incr(tl(incr(s(y0)))))) ---------------------------------------- (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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c16(MARK(adx(tl(incr(0))))) 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(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(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(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) 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(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) 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(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(0))))) -> c16(MARK(incr(tl(incr(0))))) 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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c16(MARK(adx(tl(incr(0))))) 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(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(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(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) 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(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) 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(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(0))))) -> c16(MARK(incr(tl(incr(0))))) 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 ---------------------------------------- (195) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: A__HD(cons(hd(incr(cons(y0, y1))), z1)) -> c8(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(s(y0))), z1)) -> c8(MARK(hd(incr(s(y0))))) MARK(incr(hd(incr(s(y0))))) -> c15(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(incr(s(y0))))) -> c10(MARK(hd(incr(s(y0))))) A__TL(cons(z0, hd(incr(0)))) -> c10(MARK(hd(incr(0)))) A__TL(cons(z0, hd(incr(cons(y0, y1))))) -> c10(MARK(hd(incr(cons(y0, y1))))) A__HD(cons(hd(incr(0)), z1)) -> c8(MARK(hd(incr(0)))) MARK(incr(hd(incr(0)))) -> c15(MARK(hd(incr(0)))) MARK(adx(hd(incr(s(y0))))) -> c13(MARK(hd(incr(s(y0))))) MARK(adx(hd(incr(cons(y0, y1))))) -> c13(MARK(hd(incr(cons(y0, y1))))) MARK(incr(hd(incr(cons(y0, y1))))) -> c15(MARK(hd(incr(cons(y0, y1))))) MARK(adx(hd(incr(0)))) -> c13(MARK(hd(incr(0)))) ---------------------------------------- (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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c16(MARK(adx(tl(incr(0))))) 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(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(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(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) 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(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) 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(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(0))))) -> c16(MARK(incr(tl(incr(0))))) 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)) -> 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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c16(MARK(adx(tl(incr(0))))) 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(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(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(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) 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(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) 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(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(0))))) -> c16(MARK(incr(tl(incr(0))))) 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 ---------------------------------------- (197) 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(s(y0))))))) -> c16(MARK(hd(adx(tl(adx(s(y0))))))) 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(0)))))) -> c16(MARK(hd(adx(tl(incr(0)))))) 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(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(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(s(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(s(y0)))))))) 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(0))))))) -> c16(MARK(hd(incr(adx(tl(incr(0))))))) 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(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(0)))))) -> c16(MARK(hd(incr(tl(incr(0)))))) MARK(hd(hd(incr(tl(incr(s(y0))))))) -> c16(MARK(hd(incr(tl(incr(s(y0))))))) ---------------------------------------- (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(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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c16(MARK(adx(tl(incr(0))))) 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(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(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(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) 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(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) 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(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(0))))) -> c16(MARK(incr(tl(incr(0))))) 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(s(y0))))))) -> c16(MARK(hd(adx(tl(adx(s(y0))))))) 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(0)))))) -> c16(MARK(hd(adx(tl(incr(0)))))) 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(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(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(s(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(s(y0)))))))) 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(0))))))) -> c16(MARK(hd(incr(adx(tl(incr(0))))))) 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(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(0)))))) -> c16(MARK(hd(incr(tl(incr(0)))))) 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))) 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(s(y0))))) -> c13(MARK(tl(adx(s(y0))))) 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(0)))) -> c13(MARK(tl(incr(0)))) 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(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(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(s(y0)))))) -> c15(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c15(MARK(adx(tl(incr(0))))) 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(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(0)))) -> c15(MARK(tl(incr(0)))) 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(s(y0)))))) -> c16(MARK(adx(tl(adx(s(y0)))))) 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(0))))) -> c16(MARK(adx(tl(incr(0))))) 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(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(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(s(y0))))))) -> c16(MARK(incr(adx(tl(adx(s(y0))))))) 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(0)))))) -> c16(MARK(incr(adx(tl(incr(0)))))) 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(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(0))))) -> c16(MARK(incr(tl(incr(0))))) 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(s(y0))))))) -> c16(MARK(hd(adx(tl(adx(s(y0))))))) 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(0)))))) -> c16(MARK(hd(adx(tl(incr(0)))))) 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(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(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(s(y0)))))))) -> c16(MARK(hd(incr(adx(tl(adx(s(y0)))))))) 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(0))))))) -> c16(MARK(hd(incr(adx(tl(incr(0))))))) 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(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(0)))))) -> c16(MARK(hd(incr(tl(incr(0)))))) 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